My 20 year old cat had a tooth extracted. As long as your cat is in fairly good health, she should come through it o.k. What do you mean when you say she is "fragile"? Does she have health problems?
Just make sure the vet uses Isoflurane anesthetic, and I actually think they have something even better now. This does not permeate the organs and animals wake up from it easily without lingering effects.
Give the old gal a hug from us.