Seems like the folding pistol should give the Pistol Flourish technique the Assistant Vice President uses.
Nothing for killing the AVP with folding pistol equipped - tried twice, once with ambush, once charging in. Nothing special with quick draw holster equipped, using Single Shot, Quick Shot or a variety of other ranged techniques. I had Steady Hand and Dead Man's Hand active. Any other ideas?
(Shard and Third Eye Hunter use a Blurry Quick Shot technique we've never found as well.)
EDIT: maybe using a combo of Stealth+Ranged techs?