The price you've been quoted is high, for sure. You might want to seek out a different vet.
My cat, Fang, had his front left leg amputated about two months ago because of a tumor in his shoulder. I am looking for the bills (a few others have asked about price) but I would say, in the end, I spent about $2,000 ish all together. This included two X-Rays (one to see the tumor, and other to check his lungs for cancer spread), the surgery, and a night stay at the vets. Also we had pain medications, and Gabapentin to administer to him before the surgery (to prevent phantom limb pain in the future). We really went "all out" for him, and we didn't go anywhere near $4,000. And I would have spent that, so it didn't have anything to do with me looking for cheaper prices.
So yeah, a different vet might be the best option. Do note, though, that there are some major differences in the way that vets treat pain and you want to find a vet that will try to prevent pain from occurring rather than just treating the pain once it has occurred. This will make a huge difference in recovery and your cat's life after surgery, and many vets don't have that perspective. It's kind of scary. Talk to your vet at length about it before the surgery.
If you want to know more about Fang's amputation, check out the blog I set up to help people in what is a really scary process: http://cldavis.tripawds.com/
. You'll also find the blogs of two other kitty amputation (rear leggers, rather than front leggers) on the links to the right of that blog. Let me know if you have any questions! It's scary but it's totally worth it in the end.
Oh, about keeping the stub of the other leg -- A lot of vets remove the WHOLE leg to prevent the kitty from damaging himself/herself, etc. I have talked to a few owners who kept the remainder of the legs, and the cat's seem to be fine. Fang cannot easily clean the left side of his face without using other misc objects (furniture, floor), and he probably would be able to do so if he had some arm left. However, I would worry about him getting it caught in something, cutting it open, or who knows what. Really cat's do so amazingly well on three legs, you probably don't need to worry no matter which you choose.
Hope this helps!