My cat has a cut on his leg. It's not extremely deep but its obviously bothering him. All of the vets in my area are

Customer: Hi my cat has a cut on his leg. It's not extremely deep but its obviously bothering him. All of the vets in my area are either closed or don't have any openings for a week+. I've been giving him wet food, keeping him comfortable, keeping the area clean etc. Can I use neosporin on it? Is there anything else I can do for him?
JA: Hi there. I'll do all I can to help. Is the cat bleeding at all? Any sign of swelling?
Customer: Yes he is bleeding. It's a pinkish red. I can't tell if there is any swelling, but it is warm.
JA: What's the cat's name and age?
Customer: James, 7yrs
JA: Is there anything else the Vet should know before I connect you? Rest assured that they'll be able to help you.
Customer: Okay thank you so much! He is indoor/outdoor and is a little overdue for most of his vaccines although he does have the rabies vaccine.