My cat is a reclaimed feral. She likes to play but sometimes, without warning, she remembers her wild days and will bite hard enough to draw blood. Her front paws are de-clawed but she will delibertly scratch me with her back claws. So I have been bitten and scratched many times and sometimes it is fairly deep and very bloody but I have never had an infection. I wash and put a bit of Anti-B ointment on and let the healing happen.
I rescued a big black male feral cat. Declawed him,etc. My daughter named him PIB (Pain In Butt). He could do real damage with those back claws. Really didn't care much for humantity other than one vet and myself. He loved to play with me - came up with a dozen games to play around the house. Was always stealing my personal items and hiding them in his cache. In other worlds, I had to remove underwear and bras from the drawer and put them on my body immediately. If I laid them down anywhere they disappeared. Car keys had to be put away. As for cat scratches - soap and hot water with a nail brush will take care of most of them.