Yeah, but! Korea wasn't 'declared'; Viet Nam wasn't 'declared'; Panama wasn't 'declared'; Grenada wasn't; Balkan bombing wasn't... ad infinitum.
Congress' only real say is control of military purse-strings. Without congressional approval the president can indeed act militarily, it's simply that the costs of such action will have to be taken from some other program within the defense department.
Going back to Tripoli and the Barbary Pirates, an awful precedent.