Arriving at your destination with wet trousers/skirt is certainly no one's desire, but I don't think that can be called an emergency. Worse comes to worse, you let loose and let the fabric absorb your urine.
Now, if that will potentially disable the aircraft, then it is certainly an emergency. But that's also probably an aircraft that shouldn't be aloft, because that means simply spilling a beverage could bring that plane down.
One thing to consider is that another aircraft may be experiencing a life or death emergency (more serious than wet clothing), and so your situation may receive a lower priority. And given that most ATC traffic is recorded and accessible to the public, the "I really need to wee!" emergency call will undoubtedly get a lot of attention on the interwebs.
My recommendation? Simply buy some adult diapers. They don't cost more than a few liters of aircraft petrol, and will hide any accidental spillage. Plus, they are extra cushy for your tushy, so they make uncomfortable aircraft seats more comfortable. Or so I've been told (ahem).
Or you can get a contraption that fits your man/lady parts and deposits the urine in a baggie. But do you really want to have to explain that contraption to security?
BTW, we've all been in the situation in which we suddenly need to wee. And as humans age, it typically gets worse. And some diseases make it much worse regardless of age. So ATC may be accommodating if you explain the situation and ask nicely for a priority approach.
Finally, as a pilot or a passenger, anticipating one's bodily functions is important. Few (none?) of us can do it perfectly. But keeping logs (ugh, no pun intended) ahead of your trip of what you consume, your medications, the temperature, the humidity, and how it all affects your output can really pay off. Hydration is important, but too much hydration can lead to significant discomfort. I learned this lesson the hard way by trying to watch Lord of the Rings in the center of packed movie theatre while drinking an extra large green tea smoothie. I'm normally a very respectful person, but I expected security to remove me from the building because I think I knocked over several people racing to the loo after that 3 hour horror film. It wasn't until afterwards that I learned green tea is a diuretic. My bad, and my apologies to you 22 years later if I toppled any of you over in that theatre while yelling "Make a hole!" on the top of my lungs.