Urine contains fluorescent compounds that are the result of hemoglobin metabolism, among others. If you have mice, they lack a sphincter and so dribble constantly. You can track their progress using black light in a darkened room. Scare yourself good that way.
As for radioactivity, try some lead, fishing weights or bullets or whatever lead you might find lying around. If you want shielding try lexan (tm) (plexiglass). It stops even hard beta particles if thick enough.
When I was working with isotopes we were given a Coleman lantern mantle as a check to see that the GM counter was working. Gave a nice rise in clicks. Also, be aware that "no response at all", i.e., no clicks, means the detector is swamped and you best beat a hasty and cautious retreat from the high radiation. But I'm sure you knew that.
