Wolf Knight, first make the groove and make sure it is deep enough for the wire. Then glue the 2 halves together. When you are satisfied that there is no gap, they fit properly and the glue is dry, then glue the wire in.
If you like fiddly work and have good eyesight (and the proper fine tools) you can make a staple. At both ends of the groove drill a hole. A blind hole, not all the way through. Bend both ends of the wire so the ends fit in the holes. Then glue as described above. That would make a fairly good connection, if the staple fits snugly.