Is it really so much work to grab a wad of toilet paper
, use it to wipe up the urine, and flush the t.p.? I do this in public men's rooms when I need to sit on a seat that others have stood at.
At the office, since there is one women's bathroom and a one-seater unisex washroom, I make sure the facilities are suitable for female customers after I'm done using them. (The library world tends to be mostly female, so as a male librarian I get to experience the same joys of restroom inequality that most women face everywhere else. I'm not bitter, just explaining.)
It doesn't take long, it's no more gross than wiping anything else in the bathroom, and it tends to keep people happy. And you were going to wash your hands on the way out anyway, weren't you?