Still, would you support nuclear retaliation IF there were a declaration of war issued by the congress? If not, then you are using this as a red herring, polluting the discussion.
The way I read the Constitution, a resolution authorizing the President to use force is completely within the purview of the Legislative Branch.
As I stated before, the decision as to what weapons should or should not be used in a declared war would be up to the military leaders, including, of course, the President. I would support my country in a declared war, however, as a free man, I would reserve the right to question the judgement of the leadership. That's the American way and always has been.
As to the Constitutionality of Congress giving the President the power to use force, I'll defer the final question to the SCOTUS. I doubt there'll be a serious legal challenge and if there were, I believe the SCOTUS would support the Congress.
Personally, I would save the nukes for a more solidly defined threat and target.