About two weeks ago I discovered that someone was sensitive enough to this situation to design a paper towel dispenser that gets around this problem. I can't remember where I saw this dispenser--it might have been in a restroom at the Penn Stater Conference Center. What the designer had done was to redesign the handle from the typical 1" by 1" square to a long, horizontal bar about 8" by 2". Furthermore, above the bar was a diagram of how you were supposed to push down on the bar with your entire left forearm, thereby avoiding the need to dispense the towels with wet hands. Perhaps not a perfect solution, but ingenious nonetheless.
There are, of course, far graver problems associated with washing one's hands in a public restroom. Consider the fact that after a people have used a toilet in a stall, touching or rubbing who knows what part of their bodies during the process, the first thing that they touch after leaving the stall is the faucet of a sink. (if, in fact, the person washes his/her hands--otherwise the first thing touched will be the handle of the exit door.) After washing--which could be little more than a one-second rinse with no soap--people then deposit water and whatever is left on their hands on the faucet as they turn off the water. So, there's a lot more stuff to consider before people reach for the paper towel dispenser handle.
I've devised my own OC rituals to work around such contamination worries, although when I'm in a hurry I simply choose not to obsess.