I did this. Worked great. Remove instrument cluster. Disconnect speedo cable at both ends. Remove core. Clean housing by shooting spray carb cleaner through housing using supplied straw. Using needle type tip on grease gun pump two or three squeezes into housing. Clean core with rag and apply a thin coat of grease while reinstalling into housing pushing pumped grease through the entire housing. Remove all excess grease. Reconnect ends. Reinstall cluster. Load cooler. Go wheeling.
This memory dates back quite a few years but it may be worth a shot. Years ago I believe snap on carried a speedo cable luber. Basically a a set of adaptor gizmos that screw onto your grease gun on one end and into the speedo cable on the other. Squirt squirt and your done. Don't know if they are still around.