If it has only been a week or two I would probably go with the surgery. Cancer is a horrible way to die/decline. If it has been there a while there is a likelihood it has already spread internally and I would ask for further investigation to establish this. Maybe a CT scan if possible which should give answers.
Vectis, an experienced breeder on here, has a very good article on caring for hamsters after surgery - it may not be the problem you imagine. At least he couldn't chew at it with it being his face. He may need a little collar to prevent scratching at it.
If there is no option for scans to check for secondaries I think I would just go for the surgery and keep your fingers crossed it hasn't spread but it's something that needs doing without delay really.
Caring for your Hamster after Surgery - Vectis Hamstery