Oh PinkEmily, I am sorry to hear you have had such bad news today.
I dont blame you for spoiling Chip at all, I think making her remaining time happy is the nicest and best thing you could possibly do.
I think I would give the operation a try too. If the tumour doesn't appear to be attached to anything, and the vet is confident he may be able to remove it, then I personally would give it a try. Of course, in the end it is a decision only you can make, but the way I think of it, is to look at the best and worse scenarios - the best being of course, that you can totally solve this for Ted, and the worst, well, of course is your fear about the operation and anaesthetic. Its a chance of course, that something could go wrong, but weighed against that is the chance that everything could turn out wonderfully well for Ted.
I don't envy you making the decision, and whatever you decide will be done out of love for your little guy, and so will be the right decision. *hugs*