I mean, yall go in with there with pants and leave with pants, right? Wash your hands and wipe them on your pants. Still cleaner than the alternative.

My dude, bandanas exist. Clean hands on your own bandana is as good as it gets.

Find what they call trainman, signalman or similar ones. They're bigger, tend to be easy to find in thicker fabric, and can do other jobs as well.

As you roll up to the sink, pull the bandana out, drape it around your neck. Wash, shake a little, grab the bandana and dry off.

It'll go right back in your pocket and not cause any problems very slightly damp. If need be, leave it hanging loosely around the neck or out of the pocket so it'll dry.