Also, if it's an issue of it just being "icky"
I think peeing on the toilet is yuckier. Think about it
You piss
You get urine all over your crotch
And then you wipe it away with a piece of paper. Now, if someone straight up pissed on me
I'd certainly feel a lot cleaner after shower than I would if someone just took a piece of toilet paper and wiped me off. Wouldn't you?
Nope. Urine belongs in the toilet. I wipe with paper to dry excess urine or as much poop as possible, and follow up with flushable baby wipes. I use wipes in public too. I also find that if l lean forward, I don't get much urine on myself. It hits the front of the bowl instead of my labia, and so doesn't cling there and drip back, which is what happens otherwise. I have pretty good aim. Strong pc muscles help. I have been doing it that way most of my life. When I moved in with my husband, he used to bathe immediately after a bowel movement, and then bathe again before bed. Introduction of baby wipes means two fewer showers a day in my house. So, we save water.
I shower before bed. I don't like to go outside right after I have been wet. (Comes from growing up in New York winters.) When I go to the bathroom before bed, I turn on the hot water, put my clothes in the hamper, and pee. I remove my makeup and put all the wipes and cotton into the toilet. Then I shower, exfoliate and moisturize in my shower or tub. I get out and wrap a towel around me and basically air dry. I brush my teeth, and spit into the toilet. Waterpik, then floss, and add my floss to the toilet. Whoever bathes second between my husband and I has to clean the shower and flush the toilet. It's a good system, and no one is supposed to pee in my shower. Sometimes my husband does, if I'm not in there with him. He already knows he has to clean the shower before it is my turn if he does that. Or if he jerks off. But extra especially if he plays with a toy. (That man needs to learn how to enema.)
I like our system. I feel clean in my bathroom, which is important to me. I would (and do) feel comfortable serving food that has been in my bathroom, which doubles as a proof box when I bake bread or make pizza dough. It is that clean in there. Excellent hygiene is easy. I have a hard time understanding what I view as deviations fom it. Other people are certainly free to do with their showers as they please, they just shouldn't share those showers with me.
(Though when I visit people, I usually clean their tubs before and after I bathe if supplies are handy.