Unilateral nuclear disarmament is popular in elite Catholic circles. It's supported by the USCCB, as well as noted Catholic ethicists like John Finnis, Joseph Boyle, Christopher Tollefsen, and Germain Grisez. But there are several problems with nuclear pacifism:
i) It's too late to unlearn what we know. Once the technical knowhow is out there, you can't turn back the clock. You can't make people forget how to make nuclear weapons. You can't go back to a world without nuclear weapons.
ii) If, moreover, people with the most conscience renounce nuclear weapons, then nuclear weapons will be left in the hands of people with the least conscience.
iii) It would lead to blackmail. A country that has ICBMs with nuclear warheads could dictate another country's domestic policy. It could credibly threaten to incinerate cities with impunity. There'd be no limit to the moral concessions it could extract from desperate populations.
iv) Nuclear weaponry poses a dilemma. There are no good alternatives. In a fallen world, we sometimes find ourselves backed into a corner. We face momentous hazards over which we have no ultimate control. So we must do the best we can in tough situations where the outcome is out of our hands.
Having put us in this predicament, it's up to God, in his providence, to forestall a worse-case scenario, if he so desires.