Artj, the only way I have had any luck with shift or throttle cables is to remove them to inspect the "casing" for integrity. If they were good hang them vertically and add "oil" to the cable and let gravity take over ~~ repeat ~~ repeat etc. After soaking for a few days work the cables to see if they are free. Sometimes there is to much corrosion usually in what were the "low spots and they will not completely free up. If the casing is cracked replacing is the only viable option.
Choke cables are usually wire wound and can be sprayed from the outside with penetrating oil. Removing them and hanging will also help.
However in both cases by the time they are removed for servicing it is usually easier to just bite the bullet and replace them for many more years of service
.
Dave Neptune