For those interested (or those just really bored) here is what I did.
I got some cheap 30ga stranded wire from Amazon. This was the right size to fit in the pipe. I used a piece of piano wire to get thru the neck of the lamp. The wire is silicone covered and too bendy plus the pipe is spliced between the curve and straight so there is a bump. I then soldered the 2 30 ga wires to the piano wire and pulled them thru the pipe. I then soldered up the Socket plugs and put back together.