Doesn't anyone use the salsa lid trick anymore? I did it for years, and it worked pretty well. Took a little practice, though--until you're good at it, wear shoes that you don't care about.

Anyway, if you don't know this trick, you take the lid to a tub of salsa or butter or something, and use scissors to cut it inside the groove so that you have a nice, flat, circular piece of plastic. You might need to file it with a nail file to smooth out the rough edges. When you want to pee, you curl up the lid in a U shape and place one end sorta behind your genitals--don't put it too far front--and hold it SNUGLY to your body. Then you can pee down it like it's an open funnel. But as I said, it takes practice to do it successfully.
Because the lid is plastic, pee does not adhere, and there aren't any nooks and crannies or tubes for the pee to get trapped in. You can just wave stray droplets into the john and slide the lid into your pocket or wherever you want to keep it. If you grab a few squares of TP for yourself, you can use some on the lid if you want to. Or you could slide the lid into a homemade sleeve or a folded hanky or something.
I can't remember where I picked up this trick. I'm pretty sure it wasn't in Lou Sullivan's "Information" book.
I never ran into trouble when using the men's room. But the ladies' room--no end of trouble and nasty looks and rude comments. I scared the heck out of quite a few gals. Some of them even scampered out of the women's restroom before they had a chance to use the facilities. They would hang around outside until I left. One gal saw me (I was just leaving) and was so shocked to find HERSELF in the wrong place that she promptly apologized, exited, and marched into the gents' without looking at the sign. I got out of there fast. I can only imagine the scene...I'm sure that when she saw the urinals in the men's room, she must have figured it out, but I had raced out of the building by then.
Such lovely memories. And now I want to go back to all of that? I must be mad.
No, I'm finally finding sanity after years of suppression.
How I wish there were lots of unisex bathrooms in this country.