I've never been told not to vape after surgery of any kind, and I don't know if nicotine by itself slows healing from a nerve injury.
I will say that before I quit smoking, I had some fairly annoying neuropathy that I thought was mainly from a medication I take and when I switched to vaping, said neuropathy improved a LOT.
I have to think that was due to the poor circulation I was experiencing due to my 3 ppd habit. (That's also my guess as to why wrinkles "melt" away a bit after stopping smoking.) It's like I was a wizened prune from all that tobacco and improved circulation from switching to vaping reinflated my face.
IDK how much nicotine in vaping would slow down healing period, let alone to nerves and whatnot, I really wouldn't. That said, I'm not sure many DOCTORS would either, although they probably ALL have stances on it. I mean, a more conservative doc may tell someone to halt nicotine use, whereas a less conservative one might be more inclined to say it would be okay.
I guess if I were in that situation, and I guess there may be some inferences that nicotine alone can constrict blood vessels, well maybe anyway, I would just really suggest following your doctor's advice and well if he can give you a coherent theory on WHY that might be, well so much the better.
Good luck with the surgery.
Anna