Access to no water? Unless you're very isolated, you can always get water somehow. Gas station restrooms, hose bibs behind churches, a nearby creek or pond. Shampoo as stated or Dr. Bronner's soap, rub it through the shorts and rins very, very well.

For you: try baby wipes. They're pretty good at the antibacterial thing, don't take up much space in the small sizes and they're available everyplace.