The best thing to do is to voice your anesthesia concerns with your vet. Other than that, I can only give you my personal experience with a senior dog and anesthesia.
I took in a 12 year old dachshund last year, and he needed teeth pulled, surgery to repair his upper jaw, and I had him neutered while he was under. He went through the anesthesia just fine, with no problems.
However, I was a bit worried in the beginning because of his age. I voiced my concerns with my vet, and we talked it over at length. My vet checked him thoroughly, including his heart, lungs, ect. We also did full bloodwork on him, including a CBC, a Chemistry Panel, and a thyroid check, along with a urinalysis test as well. Everything came back perfectly, so after all that, we felt he was healthy enough to go under the anesthesia. So we had the procedures done, and he did great.
So personally, I'd suggest you talk to your vet about your concerns, and I'd suggest seeing if the vet agree's on having bloodwork ran on your dog. This will tell you if their are any underlying health problems that may compromise his health while he is under anesthesia.
My friend, who has worked for my vet for years, had her 16 year old dachshunds teeth cleaned, anda f ew extractions, done last year. She also had the check-up and full panel bloodwork done prior to the procedure, and the results came back fine. The dog did fine under anesthesia.