So besides being discussed with the cats behavior what steps have you both tried to get the cat to quit. Really amputating all the cats toes should be a very last resort and not done lightly, the cat suffers a major trauma, is in excruciating pain for weeks and some never quite adjust or walk normally again.
Would you be willing to have the end joints of all your fingers cut off if your girlfriend complained your nails are sharp and your marking her arms and scratching her accidentally? The problem would be solved without you having to do stupid things like cutting your nails and filing them so they are smooth, think of all the time you will save over the years if you do.
As for the cat, does he have scratching posts and interactive toys to play with. Do you keep his nails trimmed so he can’t scratch the furniture as easily? Are you and the girlfriend giving him enough exercise to make sure he’s not bored, and is too tired to try and wander around finding things to do to keep himself occupied? Keep in mind the girlfriend and you live together, it’s no longer her cat vs not your cat, it belongs to both of you emotionally and physically but not legally. It’s part your responsibility to make sure the cats happy, had enough mental and physical stimulation to keep out of trouble. If you do nothing to work with the day or say it’s not your problem, its hers is just a cop out and giving you permission to do something horrible to a cat that fiend deserve such harsh punishment,
Talk it over with girlfriend, let her know how you feel and that your tired of everything being ruined, tell her to take responsibility for her cat and start working it, getting it toys and making it run and play, with on its hunting instincts using lures playing with the cat.
She cannot guess who’s you feel nor do s she know your this frustrated about the problems. Most people don’t wait until they start going to do something so drastic, they usually act like adults first and discuss the problem and to come up with options and solutions before jumping to huge last possible cure. Also be aware that not only the surgery is painful but many cats don’t do well under anesthesia and many die during the surgery. It’s not a quick simple routine procedure like spay or neuter.