Get the surgery. I had one on my hand and had it taken off. It was deep and left a about three inch scar because I let it get so large the surgeon had to put a lot of skin to close the gap, and that meant a lot longer scar.

The scar has faded to the point it isn't very noticeable. With a scar on her face they might be able to do some cometic surgery to hide it. It will depend on the size of the cancer how intrusive they have to be.