Moriniman's method sounds good, but getting anything that can be melted with a soldering iron to stick to stainless steel requires special flux, like Ruby's Stainless Steel Flux:
http://rubyfluidflux.com/Stainless_Steel_Flux.htmlFor stainless cables I use the
brazing rod called "silver solder", not the stuff you can melt with a soldering iron, and borax flux (make a paste with water and
20 Mule Team Borax laundry powder). Silver solder melts below the melting point of brass, so as long as the cable ends are not pot metal, you're OK if you're careful with the torch. For the small ends that go in the carb slides, you can make a blob from brass brazing rod or silver solder and shape it with a file to make your own end.
For the large cylindrical ends that go in the twist-grip, I drill the cylinder half way through with a larger drill size, put the cable through the hole, and make a brass blob with brazing rod on the cable end. Then shape be blob to fit in the larger hole I drilled, and soft solder the brass blob into the cylinder.
The heat from brazing doesn't hurt the stainless cable if you don't overdo it.