Or you could just carry wet wipes/that instant hand cleanser (I forget the name, but think it's a softsoap product), & avoid the little old lady entirely.
I always wondered about washing hands & then having to open the restroom door afterwards - who knows if the people who opened the door before you bothered washing theirs? Not to mention touching the taps (faucets) to turn them off - surely there are germs on those from dirty hands too.
Not that I'm overly uptight about these things. I saw a poster about how to wash your hands in a Memphis restroom a few years ago, & it set me thinking... according to the poster you should use a paper towel to shield your lovely clean hands from the germ-bearing taps.
I like the fully automated airport restrooms where you don't have to touch a thing. The self-flushing toilets do make me a bit nervous though....