It doesn’t really seem like it would be all that difficult if instead of gripping with your fingers curled inward, you grabbed it with the base of the last joint of your fingers, nails parallel to the wiping area.
Valete,
Vox Imperatoris
From my experience in my acrylic nails days, think of the usual motions you would use for these sorts of actions, and rotate the hand 90 degrees.
And great masturbation doesn’t necessarily involve penetration… the phrase “rubbing one out” should help you with the visual… 
Good gad, man.
Half of them wipe while still sitting on the toilet.
The other half stand up, then wipe.
Very carefully.
Now I think I might have to start a “How do you masturbate” thread for women dopers. Actually, as a female doper with a very specific way of masturbating, I have been curious about how others do it, but I’m always afraid that people will think, “Oh no–PRURIENT INTEREST” if I start THAT thread.
Well, yes. Post a link if you decide to start it. 
At home they use a bath towel like floss. In public restrooms, I’m sure you’ve seen how dirty the fixtures and walls can be at times. There is a reason not to touch the door handles.