You basically have two choices that give you what you're looking for, and that's nerve damage or incredibly extensive scarring. Nerve damage is much easier to explain, much more likely to cause loss of sensation, and much more likely to be permanent.

Crushing or cutting would probably be best ime? Ideally you'd want him to damage the internal area of his palm/back of his hand. Something like an object driven deep into/through his hand or getting his hand smashed could break a lot of delicate little bones and ligaments and stuff, and also pretty well fuck up his nerves.

I've punched glass before and unless he starts grabbing up fistfuls of it after he probably wouldn't injure his hand that badly. Even if he does, mirrors shards might not really be sharp enough to do much more than give him some wicked cuts.

Any fire big/hot enough to deeply damage his hand (which is what you'd need for a permanent injury like what you're looking for) would pretty much ignite the rest of him I'd assume. But if you like the idea of burning you could go with acid or boiling liquid of some kind. Either could do a lot of centralized damage.