Only thing that springs to mind is one of those special greasers used by motorcyclists and classic vehicle chaps that forces grease down a bowden type cable end which may force any dud grease out or at the very least lubricate the cable length? That may ease the movement of the seized part, but I’ve never actually tried it, only read similar online…

Edit: Also found THIS link which may be of help – bizzare as it looks…