Why do you think the anesthesia is a substantial risk for him? Is that per your vet? Did blood work come back that indicated that? Or is that just your assumption based on his age? I may have missed a post in the past that pointed to the answer to this question...
If he is in that much pain and a tooth has to be removed, I think your only option is anesthesia. Even if you opted for euthanasia, which it sounds like you do not want to do and feel he is not ready for, no vet in his right mind is going to euthanize a dog because the owner doesn't want to put him under anesthesia (assuming that the procedure will fix things), unless, of course, you both know for a fact that the anesthesia is most likely to cause him death.
If you do the blood work and it comes back fine, at least you can feel rest assured that he should be able to handle it. Has he been put under before? How did he handle it? Any problems? If he has been under without issue and the labs come back fine, while it's always nerve-wracking to put them under, I'd do it sooner rather than later. That kind of pain must be pretty awful for him.
Dealing with old dogs definitely has it's challenges. Give the old guy a pat for me.