A potentially big butterfly might occur in the US, where the shock of the death of a British monarch due to the war in 1940 might have broken down some of the isolationist resistance to both US aid to Britain and US preparedness, giving FDR a freer hand in preparing for what he saw as inevitable war. A better prepared US = a shorter war in all likelihood.
I'm also wondering whether the presence of an 18/19 year-old on the throne might have affected the postwar election that deposed Churchill and put Attlee in power. In a world with such a young monarch, Churchill might well be perceived as far more important to stability and therefore harder to defeat.
One thing I don't really have a handle on is whether it would affect support for the monarchy. One argument is greater support to honor the fallen George VI. The other is that having survived its darkest hour as a nation with a monarch not of age, perhaps the whole concept is obsolete.
And, residual anger over the death of George VI could result in a harsher treatment of Germany after the war. If something like the Morgenthau plan was implemented, there's no Wirtschaftswunder and a very different look to modern Europe.