If it is marked "Utica Arms Co.", compare it to a Crescent Model 6 (1903-1930) or a J. Stevens Arms Co early Model 311 (after 1920). The Stevens might even be marked "5000", "5100" or "311" on the receiver. If marked "Utica Firearms Co." or "Utica Special" it should be the Crescent Model 6. Those marked "Utica Firearms Co. London Fluid Steel" are also by Crescent, but should have outside hammers and could date back to 1892, but probably made no later than 1914. With the mark "Utica Fire Arms Co. Pat. Nov. 25, '90, March 29, '97" it was made by Hopkins & Allen Mfg Co. (1868-1898, but the patent date would indicate these guns were made in 1897 and 1898) I'm not sure if these were single or double barrel guns. All were made for Simmons Hardware 1875-1940
Actually balloon shades are a type of window shade for windows and not for lamps. They usually are scalloped and puffed at the bottom. For an example of what they look like go to http://www.boscovs.com/StoreFrontWeb/Product.bos?rch=Y&quantity=1&itemNumber=35745.