Way back, probably twenty-something years ago, Kodak came out with these things called PTRs, Particle Transfer Rollers, for taking small particles off of film. In professional finishing, these are about as close to a magic bullet as it gets.
They're some sort of rubbery material that is slightly tacky, so it is able to pick particles off of film or paper, even against the pull of static electricity. When loaded up, they can be cleaned with running water (OR roll against a more powerful tacky material).
I see things like this advertised on TV for removing cat hair from your clothes, etc., don't know if it's the same thing. Mainly, you don't want it to leave any residue behind. I'd suggest check with your photo dealer to see if they carry any such products specifically for photo use.
I imagine these will increase static charge on the paper, but so long as you get it clean, so what? As long as you have some decent level of humidity in the room, the charges should bleed off fairly quick. If it were me, I'd also go on a search for the source(s) of the specifc dust you have. Maybe you can get it under control by changing the ventilation, or something like that. It might even be from the edges of the paper if you're trimming it yourself (examine under a powerful magnifier; maybe a sharpened trimmer blade is called for). Good luck!