Andrew Cuomo, in his capacity as the governor of New York does not possess the power to declare war on Canada as this is not in his jurisdiction.
Article 1, Section 8 of the U. S. Constitution expresses that just Congress has the power to announce war, in spite of the fact that it doesn't indicate the manner by which this war must be pronounced. The Doe v. Bush judicial resolution though reasoned that an approval does the trick to fulfill this prerequisite and that a formal statement was not required.