The danger is in breathing in the dust. I use a razor saw to trim away the resin plugs and when cutting I dip the saw into some water. This makes the dust cing to the blade- next dip and the dust falls away in the water.
When sanding I dip the piece in water and then rub it on the sand paper, again -the dust clumps together and doesn't float up your nostrils
Best advice is to put the food away and wait until the children are sleeping.
Work to become not to acquire