The ship is named Excalibur. Excalibur was King Arthur's sword. So the sword with the Starfleet insignia is a symbolic representation of the ship. I think that's self-evident. Sure, maybe there could be some resonance intended with Calhoun's warrior past, but it's still symbolic.
Except that the one time we see Calhoun holding his sword on a cover -- No Limits
-- the hilt of the sword clearly bears the Starfleet insignia. The reasonable conclusion is that Calhoun added a Starfleet symbol jewel to his sword after he joined Starfleet.
To paraphrase/rewrite what my American lit professor said about Moby-Dick
, "Calhoun's sword doesn't work as a symbol if it doesn't first work as a sword."