I have slight experience with this, not precisely your situation. I had a cat with a soft tissue sarcoma (possibly vaccine related) and he was a little older than your dog (15). It was on his shoulder. I decided not to do surgery due to age and other health conditions, and because they would have had to take some ribs, and based on statements of an internal medicine specialist that he had seen cats survive a long time without surgery. Well, without surgery it grew quickly and it quickly became so large he had trouble walking. Then it also became painful for him, requiring pain injections. I'd have to check exactly, but I think without surgery he survived about 6 months, and they weren't 6 good months. Maybe 3 were good. I don't know if I made the right decision because I thought he would have a longer and more comfortable time left (without surgery) than he did, but I don't know how it would have been if he'd had the surgery, either, with his age and other conditions. Your dog sounds like he's in better health, and the surgery is more straightforward. At the same time, different types of tumors behave differently and I do not think my cat's soft tissue sarcoma is a prediction of how your dog would progress, it may be a different type of tumor. (I'm definitely not a vet.)
In the case of your dog, dogs do fine on 3 legs. The average dog carries 40% of his weight on his hind legs and 60% of his weight on his front legs. Therefore, I would think a hind leg amputation would be easier for him than if it was in front, but even front amputee dogs can still do crazy things like run in the snow.
Critters once said that dogs are born with three legs and a spare.
I think you will enjoy the pictures in this thread, a left rear amputee.http://www.handicappedpets.net/helppets ... php?t=8773
I guess in making a decision, I would ask them to tell you for sure what other options there are, and if there are any canine oncologists you could consult for a second opinion before making a decision. Since this is soft tissue, is there a way to remove the tumor and spare the bone, or is it perhaps grown into important ligaments and tendons and so forth, so he would be lame that way. In that case, amputation would be better for his mobility.
Also you want to be sure the right hind leg and hip are good enough, it sounds like they are. I assume they evaluated his right leg? And I would want a pre-screen to be sure his other organs (kidneys, liver, etc.) are up to surgery.
You might want to post on the forum over at Tripawds. There may be people there who have experience with the type of tumor you are dealing with, who can tell you how things went for their dog. https://tripawds.com/