I commend you for wanting to give this poor dog a home for the rest of his days. Diapers/belly bands with pads in them are probably your only choices since his peeing everywhere has a real physical cause. Nothing he can do about that and I hope he is not getting punished for it.
Taking on an older dog with medical problems is not an easy task. Every home is not up to the task. If your parents cannot agree with him staying, seek out a Yorkie Rescue in your area that will care for him until they find a home. Here is a link to some Rescue Information:
http://www.barkbytes.com/rescue/yorkie.htm
Bless you for your compassion.
I did have questions about ways you may have looked for his original owners. Did you put an ad in the newspaper? Flyers in vet's office, groomers, dog parks? Did you try radio stations for free announcements? How about online "found" sources? I would make sure due diligence was accomplished to find the original owners. It would be a shame if he wondered far from home and his owners had been looking in the wrong areas.