What manages the distress will vary on what it is about peeing that’s triggering dysphoria for you/in a particular moment. Sometimes it’s having to sit to pee, other times it’s feeling wetness between the folds of one’s external genitals. Sometimes it’s having to wait for the 1 stall in public toilets while there are available urinals. Sometimes it’s the fear of someone sorting out our medical history based on the sound of peeing from a shorter urethra and/or always sitting to pee and/or something else.
Things that may help:
Trust no one else is putting that much thought into how you void
No stranger is putting that much thought into if or how you pee. Maybe you need the stall to pass a bowel movement. Maybe it’s because you’re a guy who prefers to sit to pee. The only person putting that much thought into it, is you.
It’s possible some particularly nosy friend might eventually notice if you always use a stall but the only thing less likely than that, is that they would ask you about it or draw conclusions about your medical history based on that. If it comes to this, and they inquire or tease you, a firm refusal to discuss your bodily functions should suffice. It’s perfectly reasonable not to want to discuss such things.
Remember not all cis men prefer to stand to pee
There is nothing about sitting to pee that indicates your anatomy. Some cis men have urethras that end anywhere along the shaft before the tip of their glans. Some don’t want to chance having a wet fart while peeing and/or peeing while passing a bowel movement, and thus consistently sit to pee. Some just prefer to sit to pee for no particular reason.
Using a Stand-to-pee (STP) device
The cheapest is free, but it only works for some based on their anatomy: using your fingers to gently move your external genitals away from urethra and point it a bit forward. This requires comfort in handling your external genitals, having your fingers likely get a little wet in the process, and having to drop your trousers and underpants far enough to do the maneuver. But it definitely works for some people.
You can buy stand to pee devices relatively cheaply from outdoor gear stores
You can buy a stand to pee device built into a packer for a lot more
Practice in your shower, then your own toilet before rocking it out in a public facility. You decide if you feel comfortable to then rinse it in the sink, spray it with a disinfectant (while in the safety of a stall), or just slipping it back into your pants/pocket.
Some will use them in a stall, to then dry themselves afterwards. This may seem to defeat the purpose, in which case, I hope you’re not bothered by the feel of wetness.
Peeing in the shower
This may be helpful if it’s the feeling of wetness specifically on your external genitals that triggers dysphoria. This is of course, not widely available, especially outside your home. Lower surgery is the only way I know of to address this one effectively. Leave me a comment if you know of other ways.