Interesting array of responses here. I would add that aquatic organisms excrete bodily wastes into the water you dive in 24 hours a day. I'm not sure that mice are that special as to require complete disassembly and service of the regulator. I would wash and rinse, do a function check, then dive as normal.
Many of the concerns expressed here relate to the Hanta virus, a bad actor which can be spread via mouse urine and feces and can cause a fatal lung disease.