Try this
Hi Mc - What a GREAT job !
Here is another idea:
How about instead of using a hinged cap, try using a classic leaf camera shutter. (The classic camera shutter design - several overlapping metal blades which can open and close to vary the size of the aperture) . You could install a small control button on the side (the shutter will be electrically motorized). When the control button is pressed the shutter opens thus revealing the click wheel, when it's pressed again the shutter closes thus protecting the click wheel.
While being a nice concept, I would think the main problem would be to get a small enough motor inside the case...
Maybe you could do another version that isn't motorized. Maybe install a tiny lever (or a small button on a "rail"). once you move the button/lever down, the hidden mechanism opens the shutter, and vice versa.
Alon