Time pressure is more to do with taking on board that you can take as long as it takes. Anecdotal evidence of public toilets is that there is a wide range of time taken to pee: some are in and out quickly, others can be standing there a long time; the difference between them and you is that they expect to pee eventually and are willing to wait till it happens. Again this is something you can try out when desensing with total strangers.
One workshop leader uses the analogy of a car park space at the supermarket. You don’t run round the supermarket thinking “I have to release that car park spot”: no, you take as long as you want. Same with a cubicle or urinal: its yours for as long as you need it.
Standing there not peeing will be fine. One guy tested out how long he could stand there before anything happened, and gave up after 20 minutes out of sheer boredom.