Sweat contains some of the same components (in tiny amounts) that are found in urine, but it's misleading to suggest that sweat 'contains urine'. Sweat is really very clean when your body excretes it - essentially odourless water with a few dissolved salts, but after a while bacteria on the skin's surface start to break it down and that's when it starts to smell somewhat. Which, if you're otherwise clean, is really not as bad a problem as the deodorant manufacturers have brainwashed us into believing. You certainly can't 'catch' anything from sweat. I'd say the main problem with sweating on gym equipment is that it makes it a bit slippery, right? (I wouldn't really know as I'm more of a hike'nbikebunny).

Even if you did for some bizarre reason start sweating urine, it's generally pretty sterile, and rarely contains infectious organisms. It might be hard to convince the trendoids to talk to you any more though.