When I rewired my mast, I attached a shopVac to one end of the wire channel, and fed a lightweight string with a small cloth "flag" attached into the other. Sucked it right through clean as a whistle. Used that to pull a heavier cord through, and used THAT to pull the wires through.
Tip: When pulling the cable bundle through, put a small tie-wrap every 12"-18" and leave the tails on. This "spring action" will secure the wires inside the channel and keep them from banging against the sides of the channel when the boat rolls and pitches at anchor.
Bonus Tip: Since stringing wires is such a pain, While you're at it, go ahead and string an extra pair. This can be used for later additions, or to replace a failed wire down the road without having to step the mast. Leave a couple of feet exposed at the top, dip the ends in silicone to seal them from corrosion, and tie-wrap the excess neatly out of the way.