Right, done it. For future reference:
Put the shifter into top gear and push the cable from the loose end. There is a little cutout in that gear position to allow the nipple to escape through the top of the shifter. Fitting the new cable is fairly obvious, if a little fiddly to get it into the small pulley box on the rear triangle. It is a standard SA cable.
Disappointingly, I also discovered that the funky black OEM inner cables are in fact just black-painted (or maybe passivated/dyed like DT spokes) steel ones. The "kevlar" bit only applies to the outers.