Well now. According to this site http://makeashorterlink.com/?O2F013BF2 big shot, at least in the US, dates from the 1920s. Course this isn't a registered etymology site but.

PS Edit

Quinion http://www.quinion.com/words/qa/qa-big1.htm mentions it in a general discussion of "big" phrases in a specific discussion of big cheese, apparently dating it after the 1914 appearance of the latter phrase.