CLIPPER: several options come to mind. Along the lines of the SWIFFER you mentioned is this janitors dust mop/sweep.
https://www.uline.com/BL_7000/Dust-Mops. The covers are washable and can be treated with an attractant if needed. You might find something like that at a local janitors/cleaning supplies outlet. This possibility is more spendy up front than the SWIFFER but probably less expensive long term. Another thought would be to have a professional epoxy non skid surface installed to give traction even with some dust. The old school method might be to lay sand or a grit into a coat of wet floor paint, and of course that means some future maintainence possibly messy.
Just some thoughts