The correct way to handle this would be to use a disposable paper product. Most places still have a paper towel dispenser along side the air hand dryer, you're supposed to use that.
Besides the point, most people don't know how to properly wash and dry their hands. There's a technique to both that actually improves cleanliness a lot and reduces overall waste.
I never use air based hand dryers. Paper towel for life. Some places use maze patterns instead of doors, which I generally like but usually requires some extra work with air handling to make sure the bathroom air stays in the bathroom, and a bit more floor space to provide the room for the maze pattern. Those restrooms are usually the ones without paper towel, I don't mind, I just have moist hands for a few minutes afterwards.
All of this can be googled. So I won't go into more detail, but the majority of people couldn't possibly give fewer fucks about handwashing or hand drying properly. So I expect most won't even try to learn how to do things better, ever. They just go with whatever their parents taught them as a child and never question it again. Bluntly, your parents probably did the same, so you're probably working off of 50+ year old advice on hand washing.