I don't think they have or had seconds marks on the sole. The reason I say "had" is because I've installed a rubber sole on the bottom. However, I don't recall any holes, markings, or "W" on the exterior or interior of the shoe.
What I find interesting is the interior branding of the shoe, which is horizontal. Could this indicate that they were a vintage or older model? I've included a few pictures below of the branding, eyelets, and size.