The cat's tooth broke last night (it was bloody, and it seems like the broken part is dangling). Why are vets "all closed on weekends"?

I'd assume that I'd want to get an x-ray to see if there is any other damage besides just the tooth being broken.. if it is only tooth, would this mean either to get an extraction or a root canal?

Would you trust the Houston Humane Society to do this (I'm waiting for a phone call back) or.. go to a vet first thing Monday? There are a few vets that have complimentary initial exams.. does this include an x-ray?

I don't want to put the cat under anesthesia (I'm very nervous-- he once had heartworms, has tested negative since, but also has FIV; 9.5 years old)