If that's the case, how can we then explain the relevant passage in the US Constitution which allows for Congress to write out 'Letters of Marque' -- presumably to private citizens who owned seagoing cutters and pinnaces loaded with cannon?
This wouldn't apply to US Navy ships, considering that the US Constitution compels Congress to fund the US Navy.
If not the Navy, then who did the Framers intend for it to apply to?
Privateers were a sort of Naval Militia that the fedgov used as an auxillary since the Congress refused (under the Jeffersonian influence) to adequately fund a US Navy. It, at times, also forbid the arming of private vessels.
Arms generally meant small arms whereas artillary referred to cannons, etc. Arms were what the soldier carried in armies and militia while the artillary almost always belonged to the militia troop. Cavalry was also generally not militia.