My vets won't do anything in the mouth other than a quick peek without anesthesia. Talk to the vet about what they plan on doing, how they plan on restraining him to do it, and the risks they feel he is at for going under anesthesia and not having the dental done. If there is a suspicion that teeth need to be pulled, they would have use anesthesia for that so they might as well do it all right from the beginning.
I am one who has lost a pet unexpectedly to anesthesia so the idea scares the crap out of me. But I think, unless the cleaning of the tooth above the gums only part is absolutely necessary for some reason, you would be better off not doing anything if you can't do it right.