That's a tough case since you're dealing with a senior dog. I would think surgery is called for, but there are always worries about anesthesia in a dog that old. While your own vet may be uncomfortable with doing surgery, he's right in trying more palliative measures first. If this growth keeps getting larger, ask your vet for a referral to a specialist. There are plenty of universities with veterinary programs that provide outstanding specialized care - for a price of course.
If you're in the Houston area, a private hospital called Gulf Coast Veterinary Associates is a top-of-line veterinary hospital that offers every kind of specialty imagineable. They saved our dog Maggie last summer when she impaled herself on a bamboo plant stake out by the fence where she loves to jump at critters. Yep, that stake went right up her rear end and ended 10.5" into her body under her shoulder blade. Long story short, 2 surgeries, 4 days as an inpatient in ICU, and $7,000 later she was fine - and still is. Wish I could say the same for my wallet. :-) And of course, we have NO more stakes in the gardens!
I'm having the same problem with my dobi/pit mix. Aunt Jemimah is 10 years old. She has a fatty tumor near her throat ... she looks like a rooster. The vet said to leave it alone unless she has problems eating, or swallowing. It has grown, and sometimes she wakes up choking. I wish I could tell her not to sleep on her back, with her legs straight up in the air. Shes silly ! I wish you the best of luck with your dog :) Lisa