I'm very sorry to hear of Designs diagnosis
As has been said, there is no right or wrong answer. Designs chest is currently clear which is great news (if her chest was not clear, there's not much of a decision to be made, I don't think). Only YOU know your dog and if you feel that she will be able to cope with surgery and recovery and if YOU feel that she will be happy to manage on three legs, thats fine. If Design hates all types of vet visits and/or if she has other health conditions to take into consideration, then maybe amputation is not the road for you and her. But as I said, only YOU know the answers to these things
One of my own dogs was diagnosed with Osteo last October (she's a Deerhound, not a greyhound). She was 5 years old at the time and because she was otherwise healthy and because she's not afraid of the vets (etc) we went ahead with the amputation (front right) and then she had chemo and on Monday we will celebrate 8 months since the surgery. So for us, it was right.
If (god forbid, a million times) we had to make the decision again, I would do it again - if it was right for the dog in question.
Whatever you decide is right for your dog, you will get support here