You are correct. The lid under the spindle driving the speedo can be removed as you say. The spindle coming from the geardrive is a bit different. That cap, containing the grese nipple cannot be removed without damageing the housing.
I guess with the first one removed you should be able to clean most of the old gunk out, and finish it off with solvent.
You would probably not really need to remove the grease nippel cap.
Thanks to you both, the old grease has been cleaned out. I tapped out the cable drive spindle, which allowed access to the innards. All cleaned and regreased. Really appreciated the advice!