Yep, as Wim says, there is nothing in the regulations about a uniform Wintermütze with peak edging like that.
The caps on Collectors' Guild are in the same category as the cap in post #1 but despite this, his first cap is described as being a "HJ/DJ Winter Service Cap" and only at the bottom of the description do the words "private purchase" appear. Nowhere does he say that the cap is non-regulation (assuming that he knows this to be the case). The second cap's buckle is wildly different to that found on a regulation cap but this time there is no "private purchase" caveat. He simply describes it as "HJ/DJ Winter Service Cap".
He says in the description for both caps that: "The Model 1937 Winter HJ/DJ Uniform was introduced in that year, and included a ski cap similar to the "Bergmütze" worn by the army". The ski cap was originally a DJ uniform item. The HJ began wearing it as part of the skiing uniform and it would be 1938 before it was incorporated into their standard winter uniform.
My bargepole would be coming out anyway but to describe these caps in this way is unhelpful.