The only thing it’s used for in my house is to get blood out of clothes. Victims or mine, doesn’t matter 😉
There has been really no evidence that hydrogen peroxide slows down wound healing (source), because at 3% it just isn’t strong enough to harm human epithelial cells. Because we actually have enough catalase in order to prevent real cell damage from occurring. Ironically for the same reason, it does actually a pretty crappy job of preventing you against a staph skin infection, because staph is a catalase positive bacteria and also is really unaffected by hydrogen peroxide.
So using it for a typical cut probably won’t do anything at all, except break up pus or debris, which is what the AMA recommends it for. Also if you actually cut yourself out away from easy access to medical care and land into a pile of mud or manure it’s probably handy there because it will kill off the non-catalase positive bacteria really well, which is better than nothing. But something like Neosporin is ultimately a lot more effective in that situation. And in that situation please use some sort of anti-septic or antibiotic, because even if your healing time was slightly longer, it’s well worth not getting a major skin or even worse systemic infection.