cats are super adaptable, you can amputate on leg without any problem for recovery. i had to make a choice a couple of years ago between cutting my kitties front leg or letting her die of cancer, and now she is super lively and jumpy. i had to give up my pocket money for the year before to convince my parents to let her live (the ghouls) but that was possibly the best use i made of my money in my life yet.
my cat isnt in pain. she playes, has fun with my other cat, who was also kind of depressed the few days they couldnt see each others, and lives generally as well as she did before, and with less bone cancer. i dont think she would've rather died. granted, i dont think they had much of an opinion on that, but she is loved and cared for. other people in the comments can testify how animals can totally survive loss of a limb without despairing.