Sick cat

We feed a stray cat. He isn't really a stray, because we have seen him go
into another house down the block. But since he has no collar or chip, we
suspect they don't own him either. At any rate, he is sick. His thyroids
aren't working properly and he is skinny as a rail even though he eats at
least two cans of cat food a day in our kitchen alone, and God only knows
how much he eats from the neighbors. The question is, should we capture him,
give him to our roving vet to have his thyroid removed? This would cost us
around $500, but we love cats and have spent a lot more than this on them in
the past. When one of our other cats, Junie had the same problem, we paid
for her operation, and there are a lot worse ways for us to spend $500.IOW,
it isn't the money that I am asking about, but the morality of us catching
and operating on what may well be someone else's cat. I could talk to them,
but I am afraid that they will think I want money from them, and/or they may
just put poor Max down so he won't be a bother to some nosy neighbor. IOW, I
would prefer to just catch him, put him in a cat carrier, call the roving
vet, get him operated on, and let him go without ever telling anyone else
about it. What do you guys think?