The time to clean these would be whilst the strings are removed, of course. I wouldn't use a cotton bud, but rather a toothbrush (no, an old one, you fool, not the one you use every day..! Do try to keep up..! ). Mask away if you want, but a brisk brushing should remove most of the dust and surface dulling. A tiny spot of chrome cleaner, Brasso or similar might help, or even... Toothpaste..! Yes, it's a light abrasive, and won't damage anything. The headstock may smell of mint afterwards, but is that a bad thing..? A rub over with a lint-free cloth at the end and you're done..!
Hope this helps.