People,
To the O.P.'s point, I think the answer is, "yes." Cadets at Starfleet Academy probably have to learn a variety of fighting techniques, armed and unarmed.
There's plenty of evidence. Just take a look at the fight scenes in DSN's "The Way of the Warrior," and you'll see Sisko and Dax seem to know how to wield a bat'leth and how to use that weapon effectively against Klingon adversaries.
We also see in "Friday's Child" that Kirk and Spock know how to make crude bows and arrows that they use effectively against the Capellans. Survival training!
Plus I can see individual officers learning how to use a variety of weapons like different kinds of knives, swords, even bo staffs. We see that in the case of not just Worf, but Picard, Sulu, Dax, and Riker (ambojitsu (sp?), anyone?). After all, what happens when your phaser is out of power? Got to know how to kick ass, with or without weapons!
Red Ranger