Then, actually, the risk is the root cause: climate change, not nuclear war. The global war could be conventional, too. Or chemical, or biological, or genetically engineered. No matter the tool used, the risk is why they would use it vs. not using it now.

In any case, besides addressing the root cause vs. proximal cause, you couldn't even address the proximal cause anyways: it's more likely that the world could do something about climate change than about war in general.