I mean, if chemo will extend the animal's life by putting the cancer in remission, I'm in favor of it. It's a gamble that it will shorten rather than prolong the suffering, but it is with humans as well.
I mean, I get why it's appealing. My cat scratched my skin up something awful when I was younger. I still have one scar from her! But as @Pitya Ivyr said, it's essentially amputating the cat's digits, and screws up their physical perceptions as well. It's not fair to the cat. If it's rambunctious enough that the scratches (whether on humans or on furniture) are an issue, it needs better training and/or a scratching post.