Some people have found that running cold water over the back of a hand has had the effect of making it easier to start a stream. Certainly easier than taking a shower, and is something one can use in public toilets..
On a similar vein, I can take a morning dump, during which obviously the bladder is drained; then brush my teeth and the action of the brush on my gums triggers a need to wee a bit more!
Physiology is more complex than we think.
Andrew

Something interesting that I have happened upon:
I realise this is not a panacea, as it is not something that can be used in all contexts. However I have found that when I am struggling to urinate at home, squatting under a cold shower has allowed me to urinate. Having done some reading online it seems that cold water acts on the parasympathetic nervous system, which is what triggers relaxation, from what I have understood. Anyways, I don’t think I have mentioned it on this forum previously, and I thought it was worth mentioning as something interesting I have stumbled upon