If I remember correctly when I mounted mine, the back cover of the camera was removable, I remove cover, it was wired up as though it was hardwired, I undid wires, passed it through the wall, reattached wires and mounted camera, this minimizes the whole size to the size of the cable and not the plug.
Remember if the cable comes out through the back cover, to put the cover on before reattaching the wires.
Mine came out through a notch in the side at the bottom.
If you have electrical experience, the plug cable can be removed and the camera can be hardwired directly.
If you take this approach, a waterproof cover can be purchased at your local hardware store, a little silicone sealant can plug the hole at the bottom where the old cable protruded from.