Whether to use a drop spreader or a broadcast spreader depends as much on how much territory needs to be covered as what the material to be dispensed is. A drop spreader might not produce as much dust, but when I have used one for limestone there is at least enough to cover my feet while I've not had any dust, on me, from the limestone when using a broadcast spreader, but then my broadcast spreader pulls behind the tractor. A walk behind broadcast spreader may be different.
A drop spreader will cover much less territory per trip then a broadcast spreader will.