I think if it didn't even bleed, you don't have much to worry about. Since it is near the mouth, I'd skip the neosporin, which I'm pretty sure is labeled "not to be taken internally". Clean it with chlorhexidine, and just watch it closely.

Someone else mentioned cleaning it with betadine. Betadine isn't to be taken internally either, because I think it would cause iodine poisoning. However, if you can wash near the mouth without getting it in the mouth, I think that would be safe. The ointment concerns me more, because that leaves a residie that the snake could end up rubbing in to its mouth.

Chlorhexidine is definitely safe to in/near the mouth; it is used in dental offices as an oral rinse.