The in-the-hands Slip Cut is a centuries-old sleight. While frequently referred to in the old literature, handling details are generally scant. The standard handling uses the fingertips of the hand holding the deck in dealing grip to slip the top card away from the top packet. This approach was described in the unpublished MSS III, 18, also called “the Asti Manuscript”, c. 1700, p. 51 of the Pieper translation. This manuscript was translated in Gibecière, Vol. 8 No. 1, Winter 2013, p. 29-234, and later hit the printed page in Nouvelles Récréations Physiques et Mathématiques, 1769, p. 33 of the unpublished Hugard translation.
The earliest known mention of using the thumb to hold back or slip the top card was published as “The Downs Hinge Shift” in “Transposition Extraordinary” from Charles Jordan's Ten New Sleight of Hand Card Tricks, 1920, p. 10, where it is served as a variety of cover pass. (N.B. In the context of this trick, Downs does the pass with a rubber band around the packet.) In a March 7, 1924 letter from T. Nelson Downs to Eddie McGuire, he mentions doing the move as an open cut. This letter was published in The Linking Ring, Vol. 51 No. 4, Apr. 1971, p. 73.
Given the age of the Slip Cut, there has been speculation that the thumb variant likely predates Downs, but no evidence has yet been found.