If the wound is more scratch-like, I would imagine that treating it like what has been suggested would work (though, with betadine for areas away from the head I usually use a 1 part betadine 4 parts water dilution, not 1:10, and have never had a problem even on very small snakes like young garters).

If the wound is a puncture, the thing that is so worrisome isn't just that cats do tend to have a pretty high bacteria load but that the upper layers of punctures will heal before the lower ones, trapping bacteria in the wound and allowing the infection to grow where you can't get to it to treat it because the upper layers have already healed over. And you can't even tell until the infection trapped under the skin gets pretty bad.
I've had several pretty nasty injuries of that sort (not with reptiles, with myself lol) and I would have to daily re-open the surface layer of the wounds and flush them out with antibacterial stuff before re-bandaging-- I actually used my reptile first aid kit to do it! Keeping snakes comes in handy sometimes. I should have gone to the ER for those actually, but I'm stubborn.
That strategy was actually inspired by what my vet told me about a stray cat I adopted. He hadn't been neutered so he had gotten in a lot of fights and had much thicker skin than a neutered male, and had a horrible recurring infection on his neck. He told us that it had come from being punctured while fighting another cat and that the skin was so much tougher in intact males that when the surface healed over there was no way for the infection to drain out.

If you can't get to a vet, keep a super close eye on that once it heals up. Feel the area daily for any underlying swelling or hardness that might indicate an infection under the skin.