Hi Euro and family,
There is a large spectrum of “cancers” from the benign and of little concern to those highly aggressive and malignant ones. It is quite difficult to fully appreciate the best course of action without knowing exactly the suspicion/diagnosis is. The ideal scenario would be to diagnose the cancer type ( usually by biopsy) then plan surgery, getting a biopsy itself is usually an operation requiring general anaesthetic, hence the common practical path of removing the mass first ask questions later. Another option is a fine needle aspirate done conscious ( a kind of reverse injection) not always conclusive but can place the ball in the right park, worth discussing with your vet maybe.
The margins (area you remove) you quote are quite severe probably for aggressive tumours, they might not be required or as you point out, be sensible to attempt in that location.
I’d echo what others have said, if you don’t feel happy with your vet seek a second opinion, a good vet wouldn’t be offended.
She’s not that old, so try and stay positive.
all the best,
Stoat