Note that if the damage was Catch-based, then the 'borrowed Recovery power' option wouldn't work, even if you decided to nominally allow it -- because the borrowed Recovery power would automatically have the same Catch.
The Catch does not apply to Blood Drinker, though, so the BCV can still recover the minors normally, and (if you buy into the idea of long-term Blood Drinker-based healing) the supernaturally-generated 'normal' recovery should work. Though it should take as long as normal healing to fully recover (ie, to clear the slots). Taxidermy might not help much (and might not be strictly needed, for that matter). I'd definitely make sure that the BCV had an appearance-based aspect to reflect this, if it didn't already (even if this is only to prepend 'charred' to 'rotten corpse'. At best, this BCV probably needs to wear a mask to have even a slight chance of blending in.