I think you hit the nail on the head, The Hoover is by far the safest method, Don't think there can be any other way if you want to keep the dust down as much practically possible

The only real solution if your working on several floors is to get several Hoovers!! For concrete floors the idea is to get the bulk of the dust off and then just do daily sweeps with brush and a sprayer with water. You can also regulate the amount of dust created by making sure contractors use extraction and dust control equipment,i.e a hoover with a tool attachment when drill holes in floors, walls etc.. One site i visited at the end of the day cleaned and sprayed a diluted amount of PVA glue over the concrete, Next morning,not only did that stop further dust from forming but it made it easier to sweep, without making so much dust. Might be an idea??