If there must be a shit, or if there's no urinal, I use my shoe to move the seat and flush. I don't even like touching the door handle after washing my hands. I hate it when there's ONLY a hand dryer. Best designed public restrooms have paper towels as an option so you can use one to open the door and a bin right next to the door to throw it away as you exit. Otherwise it's the pinky finger handle grab.
Not to be all Howard Hughesy.