I would be interested in reading someone’s defense of the use of nuclear weapons (in self-defense) using the Catholic just war principles. I tend to doubt that it would be possible for two reasons.
First, one of the ius in bello principles of the just war theory is that a use of force has to be proportionate. The use of a nuclear weapon is never proportionate, even in response to a nuclear weapon attack. It can’t be proportionate because the effect of a nuclear weapon is not predictable. We can’t measure the damage from the heat, blast, and subsequent radiation. If a government/military launches a nuclear weapon at another State, it is not proportionate to respond to that attack by the destruction of their civilian population. Just because the aggressor failed to apply just war principles in starting the war, doesn’t mean the self-defending State isn’t morally obligated to apply those principles in conducting the war.
Second, another of the ius in bello just war principles is that the use of force must be conducted in a way that discriminates between civilians and non-civilians. Nuclear weapons totally fail in this regard.