Ever tried this?
Let the cat go into the litterbox, sit down and start to pee. This is important since it seems (at least with out Tommy) that he can't simply stop once he's started. So once he started to pee, my dh lifted his tail a little, which made Tommy lift his behind a little too, and then simply held the open urine jar under the stream! He filled almost half the jar! He looked a little bemused but didn't seem to be upset. It was rather funny to watch.
Of course, you need a really docile, relaxed and trusting cat to do this.
Nevertheless, worth a try. If my dh's theory holds that they can't stop once they start, you might get away with it with more shy and nervous cats too.