The K6 is "probably" really a K5 with a slightly deformed ricasso stamp.
I have never seen a reference to a K6 other than a couple of fleabay auctions. I have one of those because at the time I did not have a "K6" so I bought it. When it came in, I compared it to the K5 and it was a match. Under a magnifying glass it looks like you could call it either a bad 5 or a bad 6.
This was before I acquired a copy of Mr. Platts book to find out that the 1950s West-Cut K series was K1, K2, K3, and K5, the 645 and the K510, as shown in the picture above. Note: the K510 combo is the K5 knife matched with the K10 hatchet in a combo sheath. I have never seen a hatchet marked K10, either.
I would assume from the picture that the K10 would basically be an L10 with the brass spacer in the middle of the handle. At least, that's what I keep looking for.
Actually, none of the Western hatchets I have seen had either the 10 or 14 model numbers on them, except for the R10 Camillus version (see below).
Western made 2 hatchets - the 10 and the 14. The 10 is about 10.75" and the 14 is about 12.5" long.
Western under Coleman made the L10 and W10.
The advertising for the Western versions refers to them as L10, W10, F10 and F14.
The 14, only produce as the Black Beauty version (aluminum and black phenollic plastic spacers) has an I-beam style haft, similar to the Bridgeport BSA hand axes.
There was also an R10 version made by Camillus. It is marked R10. It came black-coated (probably carbon steel} and shiny, stainless versions.