Do you need to do delivery? If nuclear winter is going to end humanity as we know it, then couldn't you blow up an uninhabited wasteland part of your own country and still hurt everyone?
https://blog.nuclearsecrecy.com/2012/09/12/in-search-of-a-bi...
The scientist Edward Teller, according to one account, kept a blackboard in his office at Los Alamos during World War II with a list of hypothetical nuclear weapons on it. The last item on his list was the largest one he could imagine. The method of “delivery” — weapon-designer jargon for how you get your bomb from here to there, the target — was listed as “Backyard.” As the scientist who related this anecdote explained, “since that particular design would probably kill everyone on Earth, there was no use carting it anywhere.”
Also nuclear winter is somewhat controversial, I don’t know what the latest model results are.