Marlene, when we did this (on Viking), the ship arranged for taxis to be ready and waiting, by name, at dockside for those passengers that were not taking their extensions or airport transfers. It was seamless. The ship asked for everyone who needed such service to sign up a day or so before the end of the cruise. Undoubtedly, it will not be a problem.
The drivers will speak English - you want to go to the SBB (Swiss Rail) station across town. We paid cash (in Swiss francs because I had them), but it's highly unlikely they wont take your cards. Rail station as well, but dont be surprised if the taxi driver makes an offer to take you all the way to Luzern and quotes a competitive rate.