A flat or three dimensional body constructed of a sanitary plastic, with an inner surface of the body defining a hollow interior adapted to contact a door hardware surface or projecting knob. The body in one variant exhibits an end face from which projects an undulating and perimeter extending skirt, the design of which providing additional fabric which, upon being grasped and rotated by a user, can be circumferentially deflected and folded over against itself and the underlying surfaces of the rotatable door knob over which the cover is installed, this in order to facilitate additional frictional engaging contact with the door handle. An inside or flattened base surface of the body can also exhibit any desired tacky or adhesive material in order to provide additional gripping engagement of the handle or knob.