Remove the Socket
Loosen socket's terminal screws, and remove cord wires from under them. If lamp is small and cord goes through in straight path, slide old wire out, and feed new wire through from either end to the other. If old cord offers any resistance at all, don't tug on it. Check to see if you can disassemble lamp to make removal easier. Also, make sure cord is tied in knot to keep it from being pulled out at its base.