Oh this is so difficult. I am sorry you are going through this. It's so hard to know how a kid is going to handle it.
One option to consider is having him there to talk to the vet and have him/her explain this in "doctor terms". The vet has more experience with this than you do, and may actually be able to help assess the situation. You can still have the option of your son saying his final goodbye in the veterinary room, and be able to go out to the waiting room (perhaps with Dad or you) at the last minute if that's indicated.
One of the terms I've heard vets use is "we help the animal to die without pain instead of the way she is about to die, which is in pain." It's better than "euthanize" for some kids, and far better than "put down" or "put to sleep" for many other kids.
Our son was away at college when his dog died (similar to your situation - 14 and cancer, but she died on her own, in our arms, before we had to call the vet to do it). It was very hard for him to be away, and I still have the image in my mind of him saying his final farewell to the dog before going back to school after spring break, knowing she would not live till the end of the semester. It was awful for him - and granted he was much older than your son. Good friends of ours just went through this 3 days ago, and their 2 kids were in the room, but they are older as well.
Some things you might consider - and discuss - are taking additional photos with him and the cat (maybe making a special frame or a photo collage/memory book), what you will do about burial/cremation, and what sort of permanent marker or ceremony you will have if any (we made our own gravestone with a craft kit for stepping stones, other people plant a tree or bury the ashes with a cat toy, etc.). Also discuss what your views are about heaven, if you believe in it, or discuss a "back to the earth" cycle of life philosophy. There's a little story you can find on line called "The Rainbow Bridge" that talks about pets going to a place of no pain and being their young playful selves. For some people it's schmaltzy, for others it is helpful. You might also ask the children's librarian for some good books to read with your son to help him through this. Then there's the decision about what to do with the cat's supplies - you might pack them away for a future cat, you might donate them to a shelter, etc. We donated many of our dog's things, gave a few to friends, kept her collar and tags for ourselves, and donated leash/bowl/toys to the shelter. That can be difficult but also therapeutic - sometimes knowing the kitty's things have a second chance with needy animals can be helpful in thinking the cat is having a second life.
Whatever you do, please be on the same page as your husband (and he with you) so you can be a solid resource and comfort for your child.
Wishing you well.