You might be correct on many of the men that served later on in the unit, but some accounts seem to say different.
I have read that the men at first were hand-picked for their skills with a rifle, hence the name "Sharpshooters". I have written accounts from my own family history of my ancestor being a superb marksman and actually killing 3 deer standing next to eachother on a small rise with one shot. Whether many men of the time could do this, I don't know.
There is an account of some of the Palmetto and GA sharpshooters being placed above the Burnside Bridge. The main regiments of the PSS were not in this location. My question to you would be, Why were these men taken from their units and put with the Georgia sharpshooters above the bridge? I don't see the point, unless these men were armed differently.