Reincarnate only requires a piece of a humanoid corpse's to identify its correspondent soul, then it targets the soul itself and implants it in a brand new body. You don't resurrect your old body, you resurrect the soul.
I wonder if Reincarnate would work on Astarion?
Given it states "Provided that the creature has been dead no longer than 10 days" and being a Vampire (Or Vampire Spawn) is considered "Undead" meaning Astarion has been "Dead" for longer than 10 days, even if he's been walking around until very recently.
Yes, you could also remove the horns from Wyll
Actually you likely couldn't.
It specifies "If the target's soul isn't free to do so, the spell fails" and given that Wyll's soul belongs to Mizora due to the contract, it's not free to be taken and put into a new body. Not unless Mizora gives you permission to Reincarnate him.
Of course, if you had permission and thus could cast the spell, yes, Wyll's new body wouldn't have horns (Unless it was a Tiefling body, which would be an amusing coincidence)