A more plausible and interesting conflict is Malekith goes all in on hunting down his mother's Chaos cults and brings a massive Throng with him to kill her, setting off a international incident due to not bothering to ask the High King beforehand. Which might end up with the Everqueen approving of his actions against Chaos cultists but the High King being pissed off at the blatant disregard for his authority, setting them against each other.
That would be a huge mess to take care of, and much different than a retread of canon, especially if Albion is thrown into the mix, either as helping against the cults, disapproving of Malekith's actions, or just being the neutral party that's trying to keep the conflict below the point of drawing weapons.
It would also avoid the boring cliché of elves versus dwarves, since factions on all sides would be in conflict.
Another option is that we may well have changed things so that Malkeith isn't campaigning on the edge of the Chaos Wastes, as Dum is gone and the eastern dwarves seem to have the problem well in hand, so Malkeith and Snorri Whitebeard don't need to go up there as part of expelling chaotic remnants from the Old World.
If he's not campainging there, he won't be in the right place to find the pre-Coming of Chaos city Vorshgarr and the Iron Circlet* within, so he won't have the vision that convinces him that taking over the elves to really ramp up the war on Chaos is much more urgent than he previously thought, and also doesn't grant him knowledge of and great control over Dhar, which means he won't have the incentive to adopt the tyrannical mind set required to wield Dhar.
He's also probaly had a front row seat to see how bad using Dhar is for people's critical faculties when fighting the Fimir.
This Malkeith may well rebel, but he's likely to be much more patient about it, particularly if he sticks to Qhaysh rather than True Dhar.
A Malkeith that emerges as the champion of the colonial elves' continental legitimate grievances with distant overlords demanding obedience and taxes from Ulthuan would be very different to the one of canon, but could still produce a very devastating war, particularly if he sought dwarven allies.
Depending on where collaboraton between colonial elven mages and runsmiths goes, you could even potentially see the use of runecraft to enhance mage's skills being his replacement for the extra power from True Dhar he replied on in canon.
* One day I'd quite like to make him a wisdom granting Crown/circlet, particularly based on the revelation that Snorri Whitebeard is trying, in some ways, to be the functional parent that Malkeith has never had. A crown that serves as an angel rather than a devil on his shoulder would be a nice reversal, and would be a natural development of where we're going with Mind of Things and with the contents of the recent update. Possibly include a Rune of Fate style effect como-ed with one that grants the wisdom to use the knowledge of potential futures it grants appropriately, unlike his reaction to his canon vision of the future, where he caused what he sought to avert.
I think as an example, Snorri refusing to take a public stance despite his politics largely being self-evident is a political stand in its own right, being that Runelords should primarily focus their time and attention on helping people and their craft.
His welcoming all qualified runesmiths to learn and lecture of their own will at Khazagar is itself another statement on how he believes runelore should be exchanged - if you are qualified, you are qualified, but there should be no compulsion on teacher to teach.
Put as a whole, Snorri's chief visible political stand puts the independence of the individual runesmith to advance their craft very highly in his priorities, and his second is helping people, great and small alike. And funny enough as far as any evidence I can see, Vragni agrees on these points without reservations even if he'd rather have you pull his teeth out than say so.
TLDR - when you have this much prestige and influence, anything you do in public is a statement. Dwarves idolize the aged, the skilled, the prestigious and the wealthy, and Snorri is all of those.
I made a point earlier that I think the Ancestor Gods set the precedent that the paramount form of social influence is via the example you set rather than the words you say, and I think dwarven culture has internalised that on a deep level. Thus, the way you do dwarven politics is the way Snorri is doing it