One of my cats, then aged 14, had to have all his remaining teeth removed, even though there was nothing wrong with them. He had a chronic gum infection which had made it painful for him to eat, and after a year of getting nowhere with steroids and antibiotics that was the vet's suggestion. I was very concerned about the op, because besides his age he was out of condition due to not eating properly.
But it all went well. He still has his canines, but everything else was whipped out, I think there were 17 extractions, and of course that all required a longer anaesthetic. He came straight home, dried blood around his mouth, and immediately demanded food, clearing a full dish, his first proper tuck-in for some time.
I wouldn't worry about the extraction, and doubtless they will clean the other teeth at the same time. It won't be a very long procedure or a big dose of anaesthetic for one tooth, but if you were very worried about the anaesthetic you could ask the vet to do a pre-op blood test, to check kidney and liver functions.