Turn instead to Article 1, Section 8, where authority to issue "Letters of Marque and Reprisal" is vested in Congress. These clearly contemplate armed, privately owned ships taking on vessels of foreign powers. They would have been armed with canon at the time.
And this is not some ancient practice no longer in use. In December 1941 and the first months of 1942, the Goodyear blimp Resolute was operated as an anti-submarine privateer based out of Los Angeles. As the only US craft to operate under a Letter of Marque since the War of 1812, the Resolute, armed with a rifle and flown by its civilian crew, patrolled the seas for submarines. See Shock, James R., Smith, David R.
In this instance the privateer was not armed with a canon because it would have been very impractical on a blimp. Previous sea going privateers have been armed with canon.
Privateers were given M&R BECAUSE they were already armed. Not the other way around though.