For years I've used Lubriplate white lithium grease to lube speedometer cables, and yes you need to remove the cable from the speedometer end because there is a shoulder on the top of the cable that prohibits it coming out the bottom (transmission end).
Unless the car has tons of miles on it the housings usually stand up fairly well, 9 out of 10 times all they need is cleaned up, and re-lubricated to return to like new operation.
I used to have a tool that allowed you to lube them from the bottom end. basically a transmission drive adapter with a grease fitting that allowed you to inject fresh grease from a manual grease gun into the cable. I tried it a couple times, but got less than stellar results with it and deferred to the conventional removal from the top end, clean the cable and reinstall it with Lubriplate grease.
