If you think the cat swallowed something, isn't there some type of laxative your vet can give the cat to help it pass?
Since it isn't pooping, I'd trying something like that as a last resort. If that doesn't work, I'd suggest following Slab and Parkers advise.
Been there with my golden retiever, the last black lab I gave my dad before he passed away and it looks like the end of my 14 year old cat's run is coming very soon.
Never easy but it is the right thing to do for the animal.