Gallows Humor from Another Time Nuclear War Feared to be Imminent

Current events highlight the need for teaching about the Cold War, the logic of nuclear deterrence, the nature of high-level diplomacy, arguments for and against disarmament, the continuing challenge of nuclear arms control, and simply the utter horror of these weapons of mass destruction. I have long thought Fail Safe, Dr. Strangelove, and The Day After  are useful films for teaching those topics. But I just heard this Tom Lehrer song for the first time, and think it could be great for teaching the fear that was felt during the height of the Cold War and the impact of the specter of nuclear war on attitudes toward war in general.