Peter Reitan, "Paper Linen and Crib Notes – A Well-Planned History of 'Off the Cuff'", Early Sports and Pop Culture History Blog, 2/20/2015, following up on "The 'off the cuff' mystery", 8/16/2012:
The idiom, “off the cuff,” meaning “without preparation . . . as if from impromptu notes made on one’s shirt cuffs,” dates to the 1930s. Mark Liberman, the Christopher H. Browne Distinguished Professor of Linguistics at the University of Pennsylvania, pushed the earliest known use of “off the cuff” back from 1938 to 1936; but wondered how or why the expression came into being decades after detachable paper cuffs had long fallen out of fashion, and with no apparent immediate impetus. Charlie Chaplin’s film, Modern Times, released in February 1936 (which features a scene in which Chaplin’s Tramp writes notes on his cuffs), notwithstanding; he could not find a satisfactory reason for the decades-long gap between paper-cuff fashion and the “off the cuff” expression; none of the seemingly plausible explanation made sense. “So what happened?”
For the answer, see the rest of Peter's post.