[Arran]

The control may or may not have to be unsoldered to remove it from the chassis, but it probably will unless there is a lot of slack in the wiring. The usual trick was to solder a jumper between one side of the switch and the bottom end of the pot using that as the tie point for common negative, so the two will have to disconnected from one another. Depending on how it is constructed you will have to unbend the tabs on the front of the control to get the cover off to get at the tabs that hold the switch on, that is if the switch has to be replaced.
If you are lucky you may be able to take the cover for the pot off, and with the switch still attached, soak it in some solvents to dissolve the crud inside the switch to free it up and clean the contacts. If you are less lucky you may have to strip it down further, remove the switch section from the control cover to gain better access to the internals, which is not something you want to do if working on small mechanical things is not your forte. If you are unlucky it will be broken inside, or the switch contacts will be burned and no amount of cleaning will fix it.
Regards
Arran