I have been using the cheap Grip Shift on my commuter for years, and changing the cable is a pain. Following manufacturer directions is impossible, as far as I'm concerned.

It's been a long time, but I remember basically moving the handlebar grip out a bit and pulling the rotating shift grip straight off, away from the mount. I don't think there's any way you can get the new cable to find its path without doing that. It doesn't "auto thread" whatsoever.

But...new ones are less than $20 so that isn't so bad if a person wants to go that route.