What about the faucet handles? To you clad yourselves in paper towels to operate them too?
Well, far more often than not, I do wash my hands but with the knowledge that this is mostly a ritual without any serious prophylactic purpose. Expected behavior, and I myself expect it of me.
The chances of catching a disease from door handles and such don't much impress me. No.2 certainly has a lot more potential than No.1 for that, of course. No.1 in a healthy person is all but sterile. It stinks later on after your skin and other bacteria get to it. The exterior male urinary instrument has--barring the odd suppurating sore from STD's--nothing very alarming on it. It's far less likely to harbor disease agents than the mouth.
Your best chance of catching something from a stranger is probably touching something immediately after someone who has just wiped his eye or nose has touched it--a door handle, an escalator rail, a strap on a bus, a pen, etc. Hard to avoid. Handshakes and kisses, especially with children, are the worst.
As for toilet rituals, let's think them through seriously as if we are checking the sterile conditions in an operating room. Think about what you do, you trusters in paper towels.
If you use a stall, you should really unzip and dangle your way inside, shouldn't you? Why? Well, once you touch that--ew--door handle slathered with filth, what do you do next? Why you touch--think of it!--your zipper or buttons, maybe your belt buckle.
If you forgot to get a paper towel (if your restroom offers them) to use on the latch as you enter, you should clearly unzip before touching the latch. Otherwise, you will have innoculated your own clothing with filth as you undo your clothing in privacy. Hope you don't later touch any of those hot spots on your clothing and remember to sterilize your closures before undressing for bed.
Of course, to make the antisepsis complete, you must also emerge from the stall unzipped, with some fresh toilet paper in hand perhaps, before unlatching. Still dangling, you should make your way over to the sinks, turn on the faucets, wash all that stuff off, and turn the fuacet off with the paper towel. Only then are you free to zip up and rebuckle without the risk of smearing god-knows-what all over your clothing and whatever else you handled.
Naturally, all your own god-knows-what is all over your clothing if you don't follow a similar early unzipping and late zipping up policy at home.
Really, if contagion by casual contact were very common, the race would never have lasted this long.