Most solutions that I found required a significant change in either the connector or the cable. I’m assuming that the cable is not a variable in this case, or you’re at least hoping that you don’t have to change the cable.
A possible solution is to use the 20-position variation of the same connector, part number 1175-1667-ND, and simply leave four positions unused. I’m guessing that the extra solder terminations could even be removed, so the question would be whether or not you can accommodate the extra space to one side of the connector in your original design. In many ways, this requires the least amount of compromise compared to solutions that change both the connector and cable.