Green’s Dictionary of Slang

1. the penis [shoot v. (1a) + stick n. (1a)].

1980

Maledicta IV:2 (Winter) 192: Sometimes this process is combined with a reference to come-juice and coming – e.g. shooting stick or shooting iron, culty gun, cream-stick, cremorne = cream horn.

2. a gun [play on SE + stick n. (3)].

1845		Bolton Chron. 7 June 4/2: Every article of trading had its slang term [...] Thus pigs and potatoes were respectively represented by ‘grunters’ and ‘spuds,’ guns, powder, blankets, pipes, and tobacco, by shooting-sticks, dust, spreaders, steamers, and weed.
1846		Quincy (IL) Whig 12 Feb. 2/5: If she persists in denying our title to Oregon, may she find out Yankee shooting-sticks in full play about her form [DA].
1867		‘F. Kirkland’ Pictorial Book of Anecdotes 237/2: Sambo [...] fell back in confusion when the ‘shooting stick’ was brandished toward his own breast [DA].
1885		Bulletin (Sydney) 18 Apr. 10/2: ‘Bah,’ exclaimed the disgusted potato-skinner, as he turned back, ‘put up yer shootin’ sticks; that skirmish was all over half an hour before you came in sight.’.