I don't think so, Doyle. The only regiment providing details to guard the nitre mines in that part of the state was the 27th Arkansas, and there was no officer named Whitney listed on the rolls, which, by the way, are remarkable complete up through mid-1863 -- unusual for an Arkansas regiment serving in the Trans-Mississippi. Someone in that regiment -- the colonel or the adjutant -- was doing his job!
Turnbo, in his History of the Twenty-seventh Arkansas Infantry, makes no mention of a Lieutenant Whitney either. I don't have a clue who this officer is.