I only ever used hydrogen peroxide for bleaching my hair, and not only does it bleach things, it's stinks to high heaven as well. I'd go for the salt water - as long as it's very thoroughly cleaned with salt water, it does actually work a treat. It doesn't burn or sting, ok it will upset your stomach if you swallow it, but not anywhere near to the extent that hydrogen peroxide does. Who on earth got the idea that you should clean your mouth with something that horrid anyway?
Definitely keep an eye on it, as has been said, they're very high risk for infection as we all know that cats carry more bacteria in their mouths and under their claws than a frenchman eats disgusting foods. So the antibiotics are a good move - I think you're more likely to get an infection if you're scratched somewhere as sensitive as your mouth - I'm sure I read somewhere that it's easier to absorb stuff from there and other softer skin....... that plus you'll have all sorts of bacteria getting into the scratch every time you eat, etc.