You sound like a germophobe, to be honest. Yes, your situation is gross, but the human immune system is pretty amazing. Just look at how many people in New York City survive every day in a melting pot of subway germs.
Fecal matter and other organic waste can transmit disease and infection, especially if you get it in an open wound, but the chances of that happening if you clean and dress the wound soon after are very low. Even if a wound does get infected, we have medicine that can deal with that easily as long as it isn’t allowed to persist for a long time.
In my opinion, it sounds a little bit like you could benefit from therapy to become more comfortable with these feelings of revulsion towards normal exposure to germs. It is good to have sanitizer and stuff ready when you need it, but you also don’t need to suffer through continued panic after cleaning and disinfecting yourself from a gross exposure.
Just leave it in a random hotel room drawer—seems to be where most of them end up eventually. /s