As a starting point, I'll assume that Morathi died shortly after Aenarion's final battle or during Malekith's long absence from Ulthuan, when she was unmasked as the leader of the Cult of Pleasure by a slightly-more-competent agent of the Phoenix King.
WARNING: THIS POST IS VERY LONG AND CONTAINS OFF-THE-CUFF SPECULATION. Malekith is recalled to Ulthuan following his long sojourn in the Old World (either when the Cults of Pleasure grow too difficult to control, or shortly after Morathi's death). Allisara still leaves him, but without the goadings of Morathi, Malekith does not descend fully into obsession with the knowledge granted by the Circlet of Iron. Malekith helps to scour Ulthuan of the cults. Bel-Shanaar is poisoned by one of his own advisors, who is a member of one of the cults. Malekith takes command of the Phoenix King's armies, while Caledor is appointed as the new Phoenix King. The Elven civil war rages hot and cold for decades, with the cults forced to fight in guerilla fashion except where they are able to muster sufficient forces to mount a proper campaign. Malekith is praised for his effectiveness even as others whisper about his interest in forbidden sorceries and the brutal methods he employs to put down the cultists.
The Sundering does not occur. Despite the devastation caused by the Cults of Pleasure during the civil war, destruction on this scale does not take place. The Elves remain a functionally united race, although some renegades leave Ulthuan to establish their own fiefdoms and others remain to work Slaanesh's corruptions from within Elven society. Caledor rules effectively, and appoints Malekith as his representative in the Old World. Malekith has become so steeped in sorcery that his ageing has been greatly reduced. He increasingly sees himself as the guardian of the Elven peoples, although he is variously considered a defender of the realm and a vicious butcher whose methods are too extreme. He believes that his people are growing soft and that his actions have alienated him from them. He leaves Ulthuan again, intent on mastering his growing knowledge of the arcane and on protecting his people from their own follies.
The War of the Beard does not occur. Malekith's friendship with the Dwarfs, and his ruthless prosecution of agents provocateurs from the pleasure cults, limits the conflicts between these races to relatively minor skirmishes. When the Time of Woes begins for the Dwarfs, they are able to call upon assistance from Malekith's forces in the Old World. Unfortunately, Caledor dies shortly after the Time of Woes begins, and his successor, Caledor II, is a lesser statesman by far. Malekith's forces become depleted and are not reinforced, as Ulthuan's treasuries are spent on increasingly lavish programs to benefit Caledor II's favourites. Some Elves, worried about the decadence of Caledor II's reign and fearing the increasing insularity of the Phoenix Court, leave Ulthuan to travel to the Old World. Many join forces with Malekith's troops. Large tracts of what would have become the province of Wissenland and the Border Princes are inhabited by these Elves, who maintain strong ties with the nearby fortresses of Barak Varr and Karak Hirn. These Elves become far less refined than their Ulthuani cousins, largely by necessity. Their culture increasingly focuses on martial strength and self-sufficiency, given increased Skaven and Greenskin attacks and occasional clashes with the human tribes in the area. Distant from Ulthuan, they become less inclined to follow the Phoenix King's laws and edicts, leading to distrust and tension. Malekith is nominally the leader of these Elves, but he still acknowledges the rule of the Phoenix Court (at least in public).
The final straw comes when a number of Dwarf caravans and traders are attacked by the raider descendants of the Elves who had been part of the pleasure cults. Malekith attempts to broker a peace with the Dwarfs. His efforts are in vain, as Caledor II refuses to deal with the Dwarfs and demands that Malekith prove his loyalty by shaving the heads and beards of the Dwarfs with whom he is negotiating. Realising that this will mean war, Malekith publicly refuses to do so and announces that the Elves of the Old World will not bow to the whims of a foreign tyrant. Caledor II's armies attack the Dwarfs and the renegade Elves under Malekith, but are undone by the combined strength of their foes and a revolt by the peoples of Avelorn, Nagarythe, Chrace and Ellyrion. Even the land of Caledor turns against the Phoenix Throne. Caledor II descends into madness, ordering the sack of Avelorn as his armies march from Cothique. The Everqueen escapes to Athel Loren, along with many of her followers. Caledor II is eventually killed by his daughter, who has seen her father's insanity for what it is and has secretly brokered an accord with the leaders of the uprisings on Ulthuan.
Ulthuan continues much as it ever did, with good kings and bad. The line of the Everqueen is broken in Ulthuan, and those Elves who escaped to Athel Loren from Avelorn become similar to the Asrai. There is some tension between these Elves and those under Malekith's rule, but Allisara's unexpected return and her re-marriage to Malekith helps to smooth over these problems. Occasional skirmishes taken place between the Old World Elves and the High Elves of Ulthuan. The Dwarf realm is stronger than it would have been if the War of the Beard had taken place, and although much has been lost, the forces of Order are better-placed to resist the encroaching darkness. This becomes even more apparent as the nascent race of Men rises to prominence. Although Malekith does not trust them, having seen how readily they could be corrupted to the worship of Chaos, he is eventually persuaded by the Dwarf Kings of Karak Hirn and Barak Varr to lend his aid to the fledgling Empire. Border clashes occasionally occur with the state of Averland, but these are minor skirmishes.
The Elves of the Old World become a separate nation, culturally distinct from the inhabitants of Ulthuan. They are still few in number and surrounded by hostile forces, but can rely on the Dwarfs, the Empire, and occasionally on stranger allies. Through all of this, Malekith tirelessly protects "his" people, even as Allisara passes from old age and the task of ruling the Old World Elves falls increasingly on other leaders. There is a degree of rapprochement between the Old World Elves and Ulthuan, but relations remain cool. Neither side is willing to admit fault or to accept that the other may have been justified. Outright bloodshed is kept to a minimum. When the Great War Against Chaos begins, Malekith leads a force of Elves against the armies of Asavar Kul near Praag. They are defeated and Malekith is badly injured. Refusing to succumb to his wounds, Malekith orders the retreat. The Elves are ultimately saved by the arrival of the Dwarfs. The High King orders the forging of a suit of runic armour for Malekith, who delves into terrible sorceries to enable him to recover from his injuries. Malekith and his forces march in time to assail the rearguard forces of Kul's hordes as they march to their final confrontation with Magnus the Pious's army. After the Great War, Malekith becomes more withdrawn, a grim figure of retribution for those who would threaten the Elves of the Old World.
In the End Times, the daemons return to Ulthuan in force. Teclis schemes to re-unify the Elven peoples, while Tyrion is set on the path towards becoming the Avatar of Khaine when he fails to rescue the Phoenix King's daughter from Mannfred von Carstein. Malekith returns to Ulthuan alongside the Elves of the Old World and of Athel Loren, and his intercession enables Prince Imrik of Caledor to ascend to the Phoenix Throne following the death of Phoenix King Finubar. To bind the disparate Elven peoples together, Malekith helps to arrange Imrik's marriage to the last of the line of Everqueens, preserved by the Elves of Athel Loren. Tyrion draws the Widowmaker and begins a campaign of slaughter. Desperate for a way to stop the rampaging Dragon of Cothique, Malekith enters the flames of Asuryan in a repeat of his father's actions. He is reborn in the flames as the true protector of the Elves. Tyrion, Avatar of Khaine is brought to battle in Saphery with far less loss of life than would have otherwise occurred during the final civil war of the Elves. After Tyrion's defeat and death at the hands of Malekith, Orion and Imrik, Teclis unbinds the Great Vortex and bestows the powers of Ulgu and Aqshy on Malekith and Imrik, respectively. Despite Teclis's efforts, the winds of Azyr, Chamon and Ghur escape to empower Karl Franz, Thorgrim Grudgebearer and Orion, respectively.* Imrik becomes a blazing beacon of hope for the Elves, a reminder of the ideals the Elves strive for even as the End Times deepen. Malekith remains a dark protector of Elvenkind, an uncompromising figure committed entirely to saving his people. Teclis binds the wind of Hysh into his staff, but cannot resurrect his brother, and so finds a different hero to become the Incarnate of Light.**
Whether all of this would change the results of the End Times is a matter of speculation which I leave up to the reader.
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* = Thanks to the efforts of the Great Green Proffit Wurrzag, Grimgor Ironhide becomes the Avatar of Gork, while Skarsnik becomes the Avatar of Mork. Skarsnik is able to see the bigger picture as the End Times begin, and is so brutally cunning that he is able manipulate the cunningly brutal Ironhide into marching for "da biggest scrap in history" at Middenheim.
** = I would have had Duke Jerrod of Bretonnia become the Incarnate of Light. This is partly because I feel sorry for the guy, and partly because Bretonnia got really shafted in the End Times. Seriously, they were the whipping boys for just about everyone, from Arkhan and Mannfred to Be'lakor and Archaon. For that matter, what happened to Gilles le Breton, anyway? He came back to do... what, exactly?