Vader handily. I don't think the speed difference is that abysmal, especially considering the amount of gaps between TCW Obi-Wan and prime Vader - which I assume is the iteration being used.
If we grant Muzan usage of all his demons, then the fight is a high diff in Vader's favour. First off, his precognition allows him to sense something off about Enmu, making him the first one to die. All the other lower moons get immediately one-shot, they're comically beneath him.
From the Upper Moons, only Kokushibo matters, and maybe Akaza to some extent. Daki, Kaigaku and Gyutaro aren't touching him, ever. Gyokko isn't either, but in the off chance he does get a hit in, it's worth noting his transmutative ability is very slow acting, the hit he landed on Muichiro only transformed a small section of the anterior portion on Mui's uniform. Hantengu is trickier, but extrasensory perceptions + higher speed allows him to deal with it in a minute or so.
Dōma, despite being stronger than Akaza, is too playful and unserious, he's dying.
Akaza has a habit of retracting himself, often to perilous extent (I mean, Rengoku with a near death amp managed to restrain Akaza, forcing the latter to cut off his arm). But Akaza has some degree of outright resistance to decapitation, so he could be trickier at first. Not too much of a hindrance though, IIRC a big part of what made Sun Breeding and Red Blade so efficient is the temperature, and if that's the case then it should come as no surprise how handy a lightsaber here is.
Kokushibo is just a serious stronger Akaza with a sword, and his monster form could be an issue, but a lightsaber to the neck and using the force to restrain him is doing the trick.
Muzan is the only real hard combatant here, but he too gets restrained (after a long fight), decapitated and cut into other pieces. If he explodes, Vader uses the force to manhandle the flesh pieces and crush them to paste or just cut them. But if Muzan is lucky, he'll manage a cut through Vader's armour and his blood will damage him over time. I have no reason to think it's a oneshot though, if the slayers can resist it for sometime while weakened, then so can Vader.
If Muzan doesn't use his demons, it's a mid diff for Vader (8/10), if he does it's a high diff (6/10)
TL;DR - Precognition and TK are serious wincons for Vader. Enmu dies in one second, the other Lower moons in two or three seconds. Uppers 6 to 4 die in a minute, Doma lasts ten, Akaza lasts fifteen, Kokushibo lasts an hour and some minutes and Muzan and Vader fight either until sunrise or until Vader dices and pastes him. Or Muzan lands a hit and deconstructs Vader.
Addendum 1: This matchup may become irrelevant in the future provided there are incoming upgrades for Vader's AP due to some HR stuff.
Addendum 2: forgot to address Nakime, but if Muzan uses her then it'd be similar to if Yoriichi got into the IC, Vader gets to Muzan before Nakime has time to change the castle. If Vader finds Nakime first, he kills her (she's not physically impressive at all) and the IC collapses. Either both Vader and Muzan manage to escape or they both die in whatever void is left and it's a stalemate by definition lol.
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