I second that. Actually, I will wash my hands if the sink has a automatic motion sensor, or if the handles are levers that are easily operated with my elbow or the back of my wrist. I flush with my elbow or my foot. I attempt to not physically touch anything, except perhaps clean paper towels, if they can be acquired without touching anything else.
Getting out the door is often the hard part. If a wastebasket is close to the door, I will use a paper towel to open the door & prop it with my foot while I throw the towel away. I sometimes grasp the edge of the door, if I can get hold of it. If I absolutely have to touch the handle, I will touch it in an odd place that requires an awkward, uncomfortable grasp, as it is less likely to have been touched there. Long sleeves can be pulled down if necessary.