Something similar happened to one of my sister's cats.

She did take him to the vet since it kept on bleeding. The vet just gave him antibiotics just to be on the safe side and told her to keep the wound clean.

I think that putting some disinfectant on until the wound is fresh is the main thing you can do since they can pick up dust and bacteria just by stepping in the litter box. If you see that it's not healing properly then I would take him to the vet, my sister did take him straight away because she volunteers in a shelter and she was afraid she might have brough some bacteria home with her shoes (she often works with infected ferals).