I think you are right. If a global war happens, there will be no place to hide. It's an illusion that places like Argentina and Chile will be safe. True, they were during the World War II, but not now. The world today is too interconnected and interdependent to have a hope of hiding in some safe place during a global crisis.
World War 2 is just a war of guns and fairly rudimentary weapons, but while World War 3 will be a war with biological, chemical and nuclear bombs. Only a virus like covid can threaten the life of the whole world, it is really impossible to imagine all the other weapons activated at the same time, and what will be left of us as a species.
Anyway, we also hope that the war between Russia and Ukraine will only stop in the two countries, and not spread to other regions like the EU, otherwise, it will undoubtedly spark a third world war.