doubtful that the navy would make any effort to arm a chartered tug. Arming a ship built for commercial service requires a little more than strapping a 32 pounder to the deck. A 32 pounder weights 3 tons. The deck beams beneath it has to be reinforced as well as the frames where the gun is positioned. This work is done below deck to support the weight. A suitable magazine for the gun powder has to be built.
All you say makes sense. You have moved me towards about 80% in agreeing that the tugboats were probably not armed on April 12, 1861.
I'm not completely sold yet, but you make a very good case for it. I will henceforth regard them as probably not armed unless I find information to the contrary.