I agree on the special socket... but I've had to beat on a socket and use it that way. If you cant find the socket, Id pay someone to do it however.
When welding a nut over another one the best way to do it is to get a nut that is as large as the space will allow (including a socket) and weld it on the inside of the threads to the locking nut. Remove it with a breaker bar or long ratchet because most welds won't take much impact work. This also works for taking out broken bolts and studs. If the stud or bolt is broken off flush or below the surface use a flat washer between the nut and bolt or stud. That will keep from welding the nut to the part instead of the bolt.
Picked up one of these special sockets at O'reilly's. Worked like a charm. Thanks for everyones input.