I tried cleaning the dust off the silicone caulking on top of my
baseboards in my bathrooms and the normal dust cleaning with Swiffer
mitten doesn't seem to work at all.

I noticed that the dust accumulated in the bathrooms seem caked up,
probably due to the humidity in the bathrooms, although we do leave
the bathroom fans on most of the time until we go to sleep. The dust
didn't get into the caulking before it cured though.

Has anyone found a good cleaning agent to effectively clean the caked
up dust found as mentioned above so as not to ruin the finish on the
baseboards and the paint on the wall, or an effective method?

Thanks for your time and courtesy.