SD,
Here's how I do it:

Remove the side plate(s) to expose the gears and remove as much grease as possible with a rag and Q-tip. Then take the reel OUTSIDE and hose the works down with an aerosol engine starting fluid. This should get rid of all remaining grease and leave the reel sparkling clean. The starting fluid will evaporate in a very short time.
Be very careful with this stuff...it's extremely flammable and hard on the lungs, eyes, etc.
Lube the gears with a small amount of silicone grease.
Hope this helps....MikeT