What gauge are the wires inside? Home Depot sells cat-3 cable which is 4 single strand copper, usually used for your phone. They may have other stuff as well, but you could always run 3 separate wires if needed. I'd just make sure they are the same or better gauge.
I'd use one of the crimp connector where the silicone squirts out, like this: http://www.alliedelec.com/Search/Produc ... 00364C617F
If you are a neat freak, then solder and use heat shrink around each wire, then heat shrink them all together. Just make sure to splice them at different lengths.