for that little bit of cable, the leftover brake cable should do the job perfectly. Just make sure you get the length right. The fact that there is a bend there is not of major consequence, since it is for all intents and purposes a rather stationary bend, the radius isn't changing much as you shift throughout the cogs.
Some older bikes just used a length of coiled spring without a plastic coating on that segment. It looks cool, and it works just as well, but it's completely unsealed.