There's one person on board the Enterprise who we know for a fact is actually trained in sword combat. You'd never guess who it was if you saw only this episode.
Transcript
1
Captain's log, Stardate 5661.0. Responding to distress call from colony on Beta XII-A.
Kirk: Nobody here.
Chekov: All dead! Killed by Klingons, like my brother Piotr!
Caption: Security guy. He has one job.
2
Kirk: There are no Kling—
Kang: You are our prisoners!
Caption: {pointing at security guy} Good work!
3
Kang: You killed 400 of my crew! The Enterprise is mine. Beam us up or I'll torture your Russian ensign.
Chekov: Cossack! You killed my brother!
4
{bridge}
Scotty: 390 crew are sealed below decks, leaving 38 of us and 38 Klingons to fight it out.
Sulu: And Chekov never had a brother.
Spock: Fascinating.
5
{sword fight vs Klingons in a corridor}
Scotty: Our phasers... replaced by swords!
Kirk: Fortunately we're all trained in ancient weapons. We can all use swords.
Sulu: Not me, captain. I'll use karate!
6
{bridge}
Sulu: Helm unresponsive! We're leaving the Galaxy at warp 9!
Kirk: This plot is going at warp 9...
Scotty: The engines cannae take it! The dilithium crystals will burn out!
7
{bridge, in dark}
Kang: {over intercom} Kirk! This is Kang! I have switched off your power and life support!
Caption: Lights go out but apparently control panels still work
8
Caption: 10 minutes later:
Kirk: ... don't get life support back soon, we'll all die. End log entry.
Kirk: Right then, Mr Sulu, go see if you can fix life support.
Sulu: Aye, sir!
9
{bridge, light again}
Spock: An alien entity of pure energy us behind all this. It feeds off anger. And we have 53.9 seconds until the dilithium crystals lose all power.
Scotty: We'll drift helplessly!
10
{engineering}
Kirk: Kang! We have to stop being angry, or else we'll be doomed to eternal fighting!
Kang: Sounds good to me!
Mara: No, listen to him!
Caption: Kang's wife
11
Caption: Everyone laughs ending! (at the alien entity)
Kirk: Ha ha ha ha!
Kang: Ha ha ha ha!
Caption: {pointing at Spock} wry amusement
12
{external shot}
Caption: The energy being gives up in disgust and flees.
Caption: Roll credits.
Caption: No explanation of how they deal with all the Klingons still on board, free the trapped 390 crew, recharge the dilithium, or get back into the galaxy.