A Guy's Perspective
I feel that you should all have this from a guy's perspective, i am a guy, and I'm here to set you all straight. There is nothing wrong with wiping your penis on the hand towel. I know it sounds pretty bad but when you think about it, its actually not. This is the sequence of events that occur when I go for a pee.
Step 1: Wash hands as to not contaminate clean penis...hands are actually dirtier as they come into contact with a lot of stuff during the day, however the penis rests happily in clean underwear.
Step 2: Pee. I'm house trained so i do indeed lift the seat and close it, but only because it has a mechanism that allows you to close it without it slamming, it practically closes itself. Google: 'soft close toilet seat' for more info.
Step 3: Shake, then rinse penis head, this isn't something that you need to spend a lot of time on, just a splash of water will do, i like to think that my Mrs could surprise me to a BJ at any given moment, so i like it to be 100% clean for her, also i don't want any residue to get in my boxers. I do this at home, if i'm in a public loo, i just leave it, no big deal.
Step 4: Dry/dab on hand towel, the reason we don't use toilet paper is because it sticks to the water and then sticks to our helmet, also you have wet hands, and you cant really grab the loo roll without wetting it all, so the towel is more convenient.
There is nothing wrong with wiping a clean penis on a towel. Unless the towel is not clean.