I regularly screen gravel... was just doing it a few moments ago. A shaker, screener works for wheel barrow loads, but I suppose that's not helpful. Dust control for roads is commonly accomplished by either spraying water or by adding calcium chloride (which abosrbs water and makes the road moist).
But as for removing sand and clay, the only option is physical removal. Loosening is a physical process, not chemical.
But I recently heard about another possible option... mulch: Can I use mulch as a driveway covering? which might be of interest. Perhaps you could try it in an area to see how it does (or doesn't) affect the dust.