I don't know what you're trying to get to, but you're comparing things that are chronologically very far apart from each other. Dené-Caucasian is a (very fringe, in fact) hypothesis that is assumed to relate to language expansions that happened dozens of thousands of years ago, still in the Paleolithic era. Some of the Caucasian language families, fully formed, and very distinct from each other, are estimated to have started to split more than 4000-5000 years ago. Dené-Yeniseian is dated to at the very least 4000 to 5000 years ago. Yamnaya is just way too late for all of those developments. Yamnaya would probably have very little to do with the present distribution of the language families you're talking about even if they were ultimately related, because that link would be thousands of years before Yamnaya (and that's a really big if, aside from Starostin and some other "bold" scientists not many linguists think we can go back that far in the reconstruction of proto-languages based on a few similar roots and particles, and Starostin's work has been shown to have many mistranslations and incorrect semantic correspondences to try to force a nonexistant fit between extremely distant language families). There is no way that language families as profoundly different as Vasconisc, Yeniseian and North Caucasian (which of them? It's still very arguable if Northwest and Northeast Caucasian are directly related, actually even the two main branches of Northeast Caucasian are so distant from each other that their divergence is assumed to be extremely old, at least 4000-5000 years). I think you're trying a bit too hard to fit Yamnaya into this whole (and very controversial) Dené-Caucasian thing. Chronologically and linguistically it just makes no sense.
As for genetics, it's most likely that CWC does not derive from Yamnaya, it's actually contemporaneous with Yamnaya in the latter's mid and late phase, so chronologically it doesn't make much sense. But autosomally the steppe component in the CWC is very close to that of the Yamnaya, and their Y-DNA haplogroup was present in the Pontic-Caspian steppe that would become mostly Yamnaya roughly just before the predecessors to CWC expanded northward. So it makes sense that they were just a closely related population that probably had preserved more Sredny Stog patrilineal lineages and avoided Yamnayization by pushing northward and eventually spreading to North Europe. I find it very unlikely that they wouldn't have spoken LPIE at least when they migrated, because I am definitely not sure that all IE language branches can be derived from CWC, and I'm also unconvinced by the idea that the CWC, not being themselves a great and powerful civilization, managed to convince non-IE-speaking people to their West (BB) and to their South (Catacomb) and perhaps even some others still to speak LPIE dialects even as they were, in some cases, receding and declining (as in ~2500-2200 B.C. Central Europe).
