Is there anyone who could explain to me how a electrician could get a new wire through the wall plate, even in an interior wall, without having to do serious damage to the wall? Several people mentioned fishing wire, implying that it wouldn't be too difficult, but how do you fish a wire through a wall plate?
Cut your hole in the wall for a single gang old work box and use a flexible drill bit to drill down through the sill plate into the first floor stud bay. Measure off this hole and drill up from the basement into the same stud bay and fish your wire. Install your old work box, wire up the receptacle and you're done, with no holes to repair.