Forget the newspaper, just watch your rabbit for a few hr. Their average pee time is once every 4 hr. If he sits on a spot for several hours, take him to a litter tray w/o nothing on it, let him pee, get the sample.
If you needs a fresh sample, do the above on Mon. morning, time it just before you need to see a vet. That's how I did it last time. As soon as he pee on the litter box, get that sample, and drive to the vet. Make sure the plastic cap is screw tight and cover inside a clear plastic bag in case there is a leak.