Paul,
I checked my USSS photo database and found that the majority of portraits of sharpshooters with their Sharps rifles have them with slings attached. There seems to be a larger number of men in the 1st Regiment displaying rifles with slings; I have six photos of Sharps-armed 1st Regt. men and every rifle has a sling. Of the eight photos of 2nd Regiment men armed with Sharps, two have slings on their rifles. A sampling of eight unidentified sharpshooters with their Sharps rifles shows that only one man has a sling on his rifle. These images range from Spring/Summer 1862 to early 1864.
And below you will find a link to a document being sold by a dealer/collector in Ohio. While it lists nine new Sharps rifles, slings are completely absent.
http://www.mqamericana.com/1st_USSS_Ordnance_KIA_.html
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Brian WhiteWambaugh, White, & Companyhttp://www.wwandcompany.com----------------------------------
Randolph Mess, U.S. Sharpshooters