How to clean the tweeter or woofers?

I use a soft artist's paintbrush or a Zwiffer cloth and if the dust doesn't come off with a very light pass I just leave it there. It's not affecting the sound, after all.

short bursts from a can of compressed air. I keep a more distance from the tweeter, do to the intensity of the air, but the woofer you can get on top of. Done once a week and you'll never have a build-up. FWIW.

It probably has no effect on the sound. The weight of dust is trivial, and if it did accumulate to a significant extent, no cleaning method would be better than the vibration of use. Use will limit how much dust can accumulate. I think the situation resembles optical devices (mirrors, prisms, etc) that we have in a lab. People see dust and/or fingerprints and think they must clean them. The dust just cuts down on the brightness of the optical image when the devices are used, but has zero effect on accuracy. Frequent cleaning does damage to the devices.

It certainly happens that people think they must clean them when there's no need. Spare a thought for the audio bumpkin! A pal of mine thought he had to take a little nub of something off his B&W's tweeter and wrecked it. It was an old model and original parts were no longer available. The off-the-shelf unit he found as a replacement was an approximate match for the design, and to top it off he now had two dissimilar speakers. He wound up having to say goodbye to his B&Ws before their time.