well, what would you do?

I wasn't sure were to post this, but....
There is a cat that has been hanging around my apartment, he is very very skinny and has been desperatley trying to get onto my enclosed porch where my two cats spend their nights and eat. I don't think he is "feral" I'm pretty sure he is someones abandoned or lost pet.
Animal control has been called on him a few times by neighbors for his insistant yowling. They put up a couple traps (that havnt caught a thing and I think some kids stole a few) and havnt been back in weeks. my husband and I have been able to coax him to us a few times, if we stay with him long enough he gets pretty affectionate. The poor thing is run down though and doesn't look to be in very good health, he's very skinny and ragged, but I'm pretty sure he is fixed. We've talked a few times about figuring a way to get him into a carrier, (with some food I don't think it would be hard) and taking him to the vet, getting him checked out, and then turning him over to the shelter we got our little girl from. I've been iffy if its a good idea or not, but I know the shelter is no-kill, and id at least know the fate of the little guy. he's really not a very pretty cat, and I honestly doubt he would be adoped, but at least at the shelter he would get food, safety, and some attention.
Even though I think it would be the right thing to do for him, and id feel so much better knowing he was safe.... I'm not sure if its what I should do....
So, I ask, what would you do?

Thank you for caring, and feeding this cat.

I would try to trap the cat and take him to the vets.  (You may be able to borrow a trap from animal control or buy them at most home improvement stores or on Amazon.)  His yowling may be a sign of illness--or being in heat.  You need to confirm that the cat is fixed, and get it tested for FIV/FELK/herpes.  Depending on what the vet says, does, then you can take him to the no-kill shelter.

 Meanwhile, get some L-lysine and put it in his food.  It helps cats who have symptoms of colds and replaces an amino acid that a cat may be deficient in when sick.

Thank you so much for helping this cat. Yes, please do catch him and take him to the bet. Poor thing needs you right now. Thank goodness you have a no-kill shelter for him. Ritz is correct about the L-lysine. Any good wet food do wonders for him.