Do you have a basement? If so you could tap a wire down there and run it up through the closet wall and put a box in the wall of the closet inside the closet approx 12 inches from the floor or so, making it look like it belongs there all professional looking. Or if you have access to your attic run it down through the closet wall from the attic. Either way This takes accuracy and thought in knowing where to drill and run the wire through, but it can be done. Or if you are a little leery in doing it yourself, ask around for someone who does handy work on the side.
A lot of electricians are bear type men.
