How to clean embedded dust from old attic?

I have an old attic with a wooden floorboard and everything up there is covered in 90 year old dust(the age of the house). I want to renovate it into my new art studio so I took all the clutter out of it but I can't seem to get rid of the embedded dust in the floorboards. The wood is very old and I'm afraid to wet it and make it rot so how can I clean it without damaging the surface and spreading the dirt around even more? I want to make sure it's clean up there before putting all my canvases, drawings and art supplies up there.