Hi,
First, I am so sorry you are having to face this difficult decision. I went through this with my hound, who had a spinal tumor. I had an MRI done, and I did take him to surgery, but after about 3 hours of surgery, we found that the tumor was so embedded in the spinal cord that there would be no way to remove it without leaving him paralyzed. That was when I decided to euthanize him right there, while he was still under anesthesia.
It seems like most people here feel that it is kinder not to do the amputation, so I will just play the devil's advocate for a minute.
How is Rusty's health and quality of life, other than the osteosarc? If he has been slowing down, and going downhill for awhile, then he probably will worsen rapidly after surgery. If he is a happy healthy dog, other than this, then he might really enjoy the life he still has after the amputation. In other words, if he is not enjoying his life too much right now (aside from the painful leg), surgery might not be worth it. But if he was really happy until the osteosarc developed, then you might be buying him some good quality time.
Another thing to think about is what portion of his life is still ahead of him? If you think of one year being about 7 years to a dog, then amputation may buy him the equivalent of another 7 years. (It's another year in your mind, but another 7 to him.) If someone told you that after a surgery, you could live another 7 years, would you do the surgery? Again...I think part of that answer depends on how strong and healthy he was before the lameness started.
There is not a right or wrong answer...every situation is different. If you don't do the surgery, make sure you ask for very aggressive pain medicine for him. If something isn't working, there are many others to try. Bone tumors are very painful.
Hang in there, I wish I could help you and your Rusty. I'll be thinking about you...