Can I just say, having lost a fabulous cat 6 weeks ago to a tumour around the kidney (inoperable), and another last week to heart failure, that, however gut wrenchingly awful it is to take your beloved cat to the vet for the last time, you can console yourself (later) with the knowledge that you've done the right thing. I pushed my very emotional, in denial, DH to have the first cat put down - he was outwardly ok, but the vet was definite that he only had a week, maybe two (the cat, not DH!)and that he might not die in his sleep and that he might not go peacefully. I was going to take the cat to the vet myself, and tell DH and DS that he'd died in his sleep, during the day, although it broke my heart to think about it, but as it turned out when I told DH the terminal prognosis he was too upset to go to work, so we both went to the vet with him the following day.
Fast forward to last Wednesday night, cat number 2 (who had had a funny turn a few weeks before which I'd secretly googled as possibly heart failure and so was keeping a close eye on him) hid under our bed, and by 11pm he was breathing with difficulty. I won't go into the detail, so as not to upset anyone, but when he died, downstairs with me, at 2:30am, while I was weighing up the timescale and cost of an emergency vet, I felt like the most horrendous owner ever for putting him through that, and if that had been cat number one, who was more like a dog he was soooo friendly and loving, I'd have been even more absolutely distraught. (I hope that doesn't sound callous.)
Genuinely, I/we loved those cats, and I, hand on heart, can say that having our cat put to sleep was a mercy, and the least I could do, to give him dignity and a peaceful end, without suffering. I'm even blubbing now, writing this, but it's true.
Sorry if this is a bit over-emotional, but it's been a hell of a time, losing 2 cats in 6 weeks, having not lost any in the 11 years while I've been the "responsible adult" i.e. no parents at home to "deal" with it. I hope you can sort things out, and do what you think is right for your cat.