It's quite easy to replace - until you do, you can pull and hold the cable. A bit annoying but possible - had to do that on my old race bike.
Also sounds like the cable needs lubing, they'll corrode and get stuck over time. While you have the cable off anyway, make a small paper funnel around the inner cable and give it a good dose of WD-40. Might want to do the same with the throttle cables while you're at it