As I have said in other things I have a grandpa who hasn't taken a shower in 2 years and has a catheter that comes out all the time and urine goes everywhere. He never lets us clean it up and my 2 year old son lives here too. Now my grandpa is very mean to everyone else except my son...he wants my son to sit on the couch with him, drink out of his cups, basically just wants him around a lot. I love that he loves my son and I don't want to be rude but I have to grab my son and hold him on the other side of the room because I am scared he could get sick from my grandpa's unhygienic ways. Am I just being paranoid?
I'd also be more concerned about poop than pee.
Pee everywhere and not showering is a bit yucky. That said, in principle pee is sterile and hygiene issues usually are due to poop contaminating things...like when people don't wash their hands after doing their business.
If grandpa has a chronic catheter, however, then his bladder might be colonized with bacteria. How much risk that is for your son -- assuming he has a healthy immune system -- I really don't know. But my understanding is that in the developing world, for instance, most of the worry is due to fecal matter contaminating food and water.
Good luck working something out...maybe there's a way to get the catheter looked at so it stops coming out all the time?