Since we've strayed some, albeit with interesting sidebars, here's another non-army, non-scope tidbit.
From the February 12, 2009, page of The Word Origin Calendar:
sniper The snipe, a Eurasian bird common in wetlands and marshes, isn't the easiest thing to catch. A hunter generally sneaked up on it, disguised to blend in with the scenery, begrimed in mud and damp, and took a shot from as close as possible without alarming the bird. The term transferred to the hunting of humans in war or crime in the early nineteenth century, and the connection to the bird as been all but forgotten.