One way you might be able to capture some urine from her without having to outrage/traumatize her: Put some fish gravel in a litter box and shut her in a room with it, along with some food she loves and lots of water.
When (if?) she does go in the box, the gravel won't absorb the pee like litter does. You just pour it off into a little jar or suck it up into a syringe or such.
I meant," said Ipslore bitterly, "what is there in this world that truly makes living worthwhile?"
Death thought about it.
"Cats," he said eventually. "Cats are nice."
-- Terry Pratchett, Sourcery