As others have pointed out the huge flaw in the cross infection pathway is the door handle to exit the public toilets. Places like motorway services and airports normally do not have doors, but for others there is nearly always a door. To make matters worse the door normally opens inwards, which means you may be able to push it to get in without using your hand, but will invariably have to use a handle to pull it open to exit therefore possibly recontaminating your hand?
You can overthink what is probably more a theoretical risk than a wide scale occurrence, but the safest approach is to not have to hand touch any surface whilst in there, including taps, soap/paper towel dispensers, surfaces, door handles.
Theoretically the safest approach for a male, is to use a urinal and leave without washing your hands.
Once we get into 'number 2s' and entering the 'red zone' cubicle, then hand washing with soap for 20/30 secs is a must as well as avoiding any touching of your face. Then you just need to get past the door handle on your way out.
