How about this solution: If your face itches or something, use the back of your hand to rub it? Or some other part of your body that you can be confident isn't used to touch anything potentially contaminated.
Partition your body: some parts used for some things, others for other things. Use an elbow or knee to push buttons, use the long sleeve of a jacket as a mini-glove if you need to grasp a handle. Or wear gloves that you take off once you're inside.
I see a lot of people using their jacket sleeve to open doors or to cover a cough, etc. But how often do you wash your jacket versus washing your hands? I’d rather open a door with my hands then wash my hands (or use sanitizer if a sink isn’t around) because I can wash my hands several times a day. I can’t wash my jacket more than once a day.
Consider the sleeves of your jacket to be permanently contaminated. (Though hopefully the inside of your elbow is contaminated only by your own coughing.) Repeatedly contaminating the sleeves doesn't make them worse; just try to avoid having them touch anything else important. (Theoretically you could be worsening the doorknobs, but it seems unlikely you're adding anything they don't already have.) It may not be a perfect solution, but I think it's pretty good.
Regarding washing hands, I've found that if I do that too much then my skin (starting on the back of my hands) tends to dry out and flake off. Certain kinds of moisturizing soap are less bad at this, but I don't choose what soap is available except at home, and it has led me to find other solutions like the above.
Avoid laurel sulfate based soaps. C12 is particularly well sized to make micelles that disrupt the skin. Castille soap/ stuff made from good ol' fats and lye are the most gentle, laureth/pegylated sulfates are less-bad than lauryl sulfates.
