I've studied Civil War sharpshooter for nine years now and never came across an incident of an air power gun being used in Civil War combat (or sharpshooting). The Austrians had the girandoni air gun, but that went out of service because it was hard to maintain. It is thought that the Lewis & Clark airgun was also a girandoni, but I haven't seen it (the VMI Military Museum was closed when I went).
Airgun range is very limited. 100 yards was about the reliable maximum of the Girandoni. That's very close range considering the minie rifle could reach out to 500 yards. The Sharps rifle could reach out even further and the Whitworth could hit at 1880 yards (platoon sized target).
Check my sigline for some sharpshooting stories.
My book on the blackpowder sharpshooter should be out in a month's time. It's 7 x 10, 856 pages, fully indexed and has over 150 maps, illustrations, photos. The text is close to 400k words.