To clean tweeters I have VERY VERY VERY gently used Scotch tape to lift dust and lint. You want the tape to barely make contact with the tweeter surface. Painters tape might be better since the adhesive is less sticky. With a hard dome I imagine you can use a Q-Tip to gently clean it. The surrounds are trickier, but I have cleaned them with the tape method to lift debris out. Just take your time and use a steady hand.