You can get a "torch" butane lighter, such as this:
http://www.lightersdirect.com/Cigar+...ack.14573.html
..and use it to heat the cable end red-hot. Then dab on a bit of solder (I don't use any flux). I do this to feed a new cable thru SRAM twistie shifters. They're tricky, IME.
(I don't prefer this lighter, but grabbed a quick link to demonstrate the low cost
)