I can only think of one thing that isn’t too drastic - namely getting creative with a vacuum cleaner, some tape and a straw or piece of rubber hose.
Rig something up that allows you to use the hose as a nozzle, whip a bulb out and feed that through the hole and suck up as much dust as you can! Just watch the end of the straw/hose isn’t going to scratch or leave any marks...