Should I have surgery on my elderly cat?

My geriatric cat (19) has been losing weight and is very skinny. She has been this skinny for a year. She has had some bouts of diarrhea and vomiting but not frequent. I thought most of it was hairballs so shaving her fur has helped. She seems alert and generally healthy with a big appetite. We've had blood work and Xrays, but show no sign of cancer. However the vet suspects cancer because of her weight. There is a tumor that is in the skin near the shoulder blade that is not attached to anything. We are thinking of having it removed. However, she also has a heart murmur. The odds of getting that tumor out successfully are pretty good but she still may have an underlying cancer, in her intestines for example. We were trying to save her from the suffering of cancer by removing the skin tumor, but it sounds like it's elsewhere too. If it was you would you go ahead with removing the skin tumor?