When I need to join two wire ends together, I usually use a butt-connector (restrain yourself linc):
http://www.radioshack.com/product/in...ductId=2103512
I remove the plastic covering, tin each end, tin the wires, and heat up the connector and wire and it will slide right in. Once cooled, heatshrink the join. If done right, the join looks pretty seamless because the connector wall thickness is just a little thicker than the wire insulation so only a slight bump is visible.