There is nothing unusual about a line cord from this sort of fixture. Some Fl. fixtures can be purchased with a simple factory installed line cord. Just be attentive in doing same and make sure there's a strain relief on the cord. By the way, where else but from the ceiling would you mount it?
Be sure the power cord doesn't catch on sharp metal edges. You can use a clamp that screws into the 3/4 inch or so round hole that most fluorescent shop light fixtures have for stringing wires through, and this protects the cord.
When cleaning anything including baby diapers, it is better to sweep off or scrape off as much solid and semisolid material as you can first. (1) Less cleaning fluid or detergent needs to be used, (2) Less of a mushy mess which in turn means that bleaches or disinfectants will be more effective.