Washing a cat is a hard thing to do. My cat hates it when I come at her with a pair of scissers. I have been lucky because my cat is relatively easy to keep still for short periods of time. My vet was somewhat uncomfortable when I admitted that I do this. She felt that I might accidently hurt the cat. I told her that I can't be by her with her butt smelling like that. If she is going to live with me, I have to clean her butt sometimes for her. I suspect you feel the same way.
I think the idea of checking her in the morning and taking her in if it looks bad is a good idea. I can't rush my cat to the vet anyways because I don't drive. It's probably just a simple cut and will heal quickly. I hope it works out very quickly for you and your cat.