Here is my Pentel W-Knock mechanical pencil. Not much is known about this model and it is a very rare find. There was a comment on Reddit that potentially explained the “W” reference…
“I don’t know any Korean, but I know about W and double in Japanese, so here it is in the hope that it
might help: AFAIK Japanese people read the letter ‘double‐u’ and ‘double’ the same (as ‘da‐bu‐ru’) because the ‘u’ at the end is silent (or just makes the ending ‘u’ sound a bit longer). So, in some cases the letter ‘W’ is used instead of writing
the word ‘double’.”