Dust enters a Voyager around the seams in the case halves, not the keyboard which is sealed with a rubber gasket.
Using a very small flat screwdriver, lift the four rubber feet off the bottom. Remove the four screws (probably #0 Phillips but may be torx T6) and lift the case back off. Remove the two very small ESD springs from the top left and bottom right sides, they are inside a small molded tube. The longer one lives next to the battery holder.
You'll see one of two version units. The early units have the logic module encased in black plastic anti-static film. The later units present a bare pc board. The early units can be disassembled a bit further by removing the logic module and you'll have access to the window and lcd to clean with canned air and some glass cleaner. Don't rub hard on the lcd, the polarizer is soft and scratches easily.
The later one board models - are tougher. You can blast with canned air around the lcd to remove dirt specs. If you have any stubborn specs, use a strip of coated slippery paper (the backing paper from a label works well) to slide down from the top and dislodge the stubborn bits. Again, the polarizer is soft so be careful.
Once clean, pop the springs back in, cover on and stick the feet back on. Should be good for another 20 years.
Pioneers with that nasty lcd cover - shoot the canned air in the side seams of the case. You can also try in the battery compartment directed down the two metal contacts as the case is open to the lcd in that area. With patience, you can slip a piece of coated paper in from the side if you have nasty hangers on.
The final solution: several cycles through an ultrasonic cleaner takes care of all dirt if you have one handy.