Therefore, might your “swan hyphen” be a corruption of an original term “swung hyphen”?
"#" was another one with many names that have consolidated over time, been decades since heard anybody refer to it as a checkerboard, which was never as elegant and can see why "hash" became the norm.
# Common: number sign; pound; pound sign; hash; sharp; crunch ; hex; [mesh]. Rare: grid; crosshatch; octothorpe; flash; <square>, pig-pen; tictactoe; scratchmark; thud; thump; splat.
http://www.catb.org/~esr/jargon/html/A/ASCII.html
So, according to the above, the most common name for # is “number sign”, and the officiall ANSI/CCITT term is “square”.
Also, in the 1975 movie Three Days of the Condor, the term “symbol for number” is used, presumably referring to #.
Also, I remember * being "splat" back in my PR1MOS and Vax days.
Sometimes single quotes to me are "ticks," with the grave accent being a "back-tick."