We used one of those shallow rectangular ziploc containers to catch my Hav's urine. It worked fairly well and there was a bigger target that we needed him to hit to get a sample.
My vet always did the needle aspirate on my cat, who had urinary issues when she was a kitten. She just grumbled a bit, not even a hiss.
I am sure you all are going to think I am beyond stupid (won't be the first time you've thought that, I'm sure
), but when they puncture the bladder with a needle, what prevents the urine, plus bacteria if present, from leaking into the abdominal cavity?