Life isn't fair. You could possibly get away with not listing them on the application if it just refers to a police record and makes no mention of "expunged charges." However, you WILL have to list it on your SF-86 which goes along with your application to the board so you might as well remain consistant.
Even hadn't you been convicted, you would still have to list the original charges on your security clearance form. Just google SF86 and you can see what it looks like. Any police involvement will require the date of the offense as well as the disposition of the case, even if all charges are dropped.
Fair to you isn't what they are after. They want to know the background of the potential officers who will have our soldiers, seamen, and airmen's lives in their hands.
Just be completely candid and everything will be fine. They aren't out to get you, just to get to know you