A 3 wire dryer circuit is X-Y-N (usually red and black, and always accompanied by white).
Optional grounding may be accomplished by daisy chaining a separate ground wire from the dryer frame to a known ground.
A 4 wire (including ground) dryer plug may not be connected to a 3 wire circuit (without ground).
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.