I'd just keep an eye on it. If it seems to be aggravated within the next few days go get it looked at. Other than that just keep it clean and disinfected like you would any other cut or scratch.
Also, if this cat looks so well cared for, are you sure it hasn't just gotten lost? There might be a family looking for it right now, I would recommend posting a clear picture and description online somewhere, or in a local paper. Also, perhaps take it to the vet to check for a microchip? I've lost a cat before and it turned out it had been living with a family who lived a couple of roads down from me. They only got it checked for a chip when they went to get one of their own put in!
As for taking it to a shelter, I would echo what other people have said. They are sometimes too quick to euthanize, so perhaps keep it for a week if you can and advertise yourself?