I can’t speak for all men, Red, but I learned early on not to pee on my hands–although I do confess to playing target practice with the urinal deodorizer cake regularly. Nevertheless, I DO wash with water and soap (when the dispenser contains some) and try hard to dry my hands, as do MOST of the men I encounter in shared access restrooms. More often than not, my intent to dry is frustrated by finding towel dispenser(s) empty. Perhaps THAT’s why you find wet door handles in restrooms!

I admire your heath consciousness. Hand sanitizer is a good investment for us all. I carry it routinely in my pocket and car.