Make your own "Better than Swiffer" Dusters. Microfiber seems to work best, it really grabs the dust. You can usually finds sheets of it in the car cleaning section. You can also easily make swiffer mop covers too, by just measuring a rectangle about twice as long as the mop, folding over the ends to fit it and sewing them in place.
The Rubbermaid Commercial Products HYGEN Double-Sided Rough Surface Scrub Microfiber Mop Head Case of 6 describes the product details with vital specifications. It is antimicrobial and includes mop pads.