I'm not a medical expert, but typically your skin is pretty good at keeping pathogens out, at least when you clean yourself regularly.
Keeping your hands clean (and thus your eyes and mouth) should be a priority. A relatively cheap and easy thing to focus on would be cheap, disposable gloves. Buy them in bulk, and carry a wad in a pocket. You can turn old ones inside out and use them as little trash bags. Change them out whenever you feel like it.
If you don't have a clothes washer at home, consider buying a cheap portable unit that can drain into the shower or sink. I have one, and it rocks.
You might feel a little crazy, but if you have the spare cash, buy some bleach spray and paper towels and wipe down the elevator. It should only take 5 minutes. It could be the case that it only needs to be cleaned every few weeks.
Remember that by keeping your space and person clean, you are doing a lot to stay healthy. People work draining septic tanks for a living and are exposed to sewage, but stay healthy because of good hygiene habits in the long term. I don't mean to minimize your situation, because I'd feel crazy too, but just keep in mind you're already doing a good job.