*Go ahead and patch the wall using the drywall piece that you cut out. No need to put a blank cover over it after it is patched, sanded and painted.
If you located the wire next to a stud you can slide the box over so part of it is over the stud. Drill two holes in the back of the box so that you can screw it to the stud. You may have to drill pilot holes through the stucco for the wood or sheet metals screws to catch the wood stud. Use a masonry bit for drilling through the stucco.
If you are not located close to a wood stud, you can use plastic anchors and sheet metal screws. Use the correct size masonry bit for the anchors. A
1/4" bit is used for #10-12 anchors.Put duct seal in the hole behind the box where the wire comes through to prevent air from leaking inside. Caulk around the top and two sides of the box after you mount it. Do not caulk the bottom. Lately I have been using GE Silicone 2 Gutter and Flashing caulk. It remains very pliable after it cures, but it is not paintable.