Hi! I have an external back door that the handle latch is missing, and the handle is simply flopping out of the hole cut in the door. I dont know if I get a new door handle set like this, or this will it fit in the existing hole? I feel that the existing hole is a bit worn away. In this case could I use one of these square reinforcement plates or a round reinforcement plate? If so, how do you know that the knob size matches the plate size? Thanks so much for your help!