I only have legitimate experience using the Peecock (which is quite a bit different from the medicine spoon and nipple style STPs, or the sort that one keeps in their pocket), but from my understanding the key is primarily: practice, practice, practice before attempting the urinal.
I was one of the fortunate ones (it seems) in regard to the Peecock because I got the hang of it very quickly, and while I haven't attempted a urinal I have used the toilet at home and (mostly) used it outside on a backpacking trip on which I was stealth with nine other guys (the only person who knew was the professor/instructor). There was some adjusting, but really not enough to be suspicious, and most of it was just whipping it out with some positioning at the end so nothing that really looked like I was groping or anything that seemed weird. Once you get the hang of where the receptacle part needs to go, things seem to go pretty smoothly.
With a urinal, it's mostly aim, which you can practice pretty safely with your home toilet (or even the shower): imagine a target if it helps, or use the drain as a target -- that improves cis guys' aim as well.
What may help regarding the fiddling around and such is to not necessarily bother with using the flies: I just undo my pants, push my briefs down enough to pull it out, position, and go. Of course, as mentioned, I wear briefs (boxer briefs or just briefs), so if you use boxers they might be easier to use the fly on. I haven't attempted that, however.
