The problem is that people leave their computers on at night and you do not want to activate or change anything on people's computers. The problem is lessened if you pick up the mouse in your hand off the desk to clean it. Make sure that you are not touching the bottom of the mouse. Keep it off any surfaces. Watch the monitor to see if you are affecting anything. It is safer if the computer is powered off of course.
I use a damp microfiber cloth to rub clean the surface. You may want to use a small toothbrush for crevices.