Personally I'd want to get the old liner out.
I had a thought on how you could do this but it's just a thought.
Cut the end off a cable crimp so it's hollow. Slide it on and rimp this on to the cable way up so you have lots of spare cable. Pull it through, hopefully it should then allow you to pull the sheath out a bit and remove .
Reverse the pull, remove the crimp, slide new sheath over and through to the other side.
At this point I'd remove the cable and flare the sheath somehow so it doesn't pull through, then refit the cable.
Like I said, a thought that may work in practice.
