If a world war starts and one of those old farts remembers to use nukes, it will not be only Bitcoin that will be disappearing. It will be the end of the world as we know it. Bitcoin would be the least of your concerns in the that scenario...
it is clear that in a war situation there will be many obstacles that will be ahead, it is certain that everyone will no longer think about bitcoin and everything, because everyone will be focused on the war. not yet with the possibility that the internet network also cannot run normally and there will be no transactions or anything to be able to make bitcoin transactions.
obviously any war will affect bitcoin especially if it comes to using nuclear which will obviously destroy world civilization and where there are bitcoins in it, everything will disappear from the face of the earth.
To put it simple, people would mind surving and living more than anything else. During a war, monetary systems or money itself will be useless because a total havoc is more likely to occur. This includes Bitcoin and other virtual currency. It will remain on your wallet but it would more likely have no value because there won't be a demand on it. So it will just be something of an amount which would be useless during those times, which I hope won't happen in the future. The market and economy will recover but expect that after a war, there would be years before majority of destroyed establishments be restored.