Some advice for the men's room
1) when entering do a quick scan. Try to avoid eye contact but if you do, offer a quick nod to acknowledge him and then continue scanning.
2) unless you enter with a friend, don't make small talk with other guys. Guys are there to do their business and leave.
3) When at the urinal don't look around. Most guys look down at themselves, straight ahead, or up at the ceiling. Guys will have a problem if they notice you looking around or looking at them. Some privacy is appreciated. This also means they won't be paying much attention to what you are doing.
4) Most guys will use their hands to shield themselves. Most won't really notice the lack of anything especially if your hands appear to be in the correct area. I honestly wouldn't expect anyone to call you out on a lack of a penis unless you were obviously doing something out of the norm. For example, standing in two feet in front of a urinal with your pants and underwear around your ankles.