Small arms in the Wing Commander Universe is something that gets a lot of mention but hasn't really been catalogued properly yet. So... lets do it here!
I don't have Wing 3 or 4 with me, so someone else will have to go through those videos for the guns that appear. Here's what we see in Wing Commander Academy:
Several marines (including the Sergeant and Paz) have these sidearms in the Repleetah scene. They're never used, so we don't know exactly what they are - just that, based on the grip, they're different from the "Space Forces" sidearm seen throughout most of the series. They may be the same as the 'Navy Sidearm 2' (explained below).
This is the weapon that most of the marines use in the Repleetah scene. It's also the "souvenir of the corps" that Paz keeps in his fighter, and when the Space Viking is under heavy guard this is the weapon shipboard security uses. They fire an energy blast, presumably a laser. The Kilrathi use a very similar gun at some points later in the series.
Edit - Paz actually calls this a laser rifle.
Satchel charge! Paz uses one to blow up a Kilrathi tank.
One of the marines in the Repleetah sequence uses this to blow a Kilrathi tank in half. Fires an energy discharge of some sort.
This is the rifle used by shipboard security on the Tiger's Claw in all instances other than when the Space Viking is being guarded. The security guards who try to subdue Maverick et. al. in Most Delicate Instrument are carrying these, and they're also the type of weapon used to subdue the Space Viking when he first arrives. They fire some sort of energy which stuns the victim.
This semi-automatic looking gun is seen very briefly in the first episode; the security guard at the Flight School is holding one.
This is the standard Navy sidearm. It shows up in several episodes -- Burroughs uses it to disarm (kill?) a Marine in Red & Blue and the heroes carry them in all the 'ground' episodes.
This is the 'sniper rifle' which Paz carries with him in Lords of the Sky. It fires a laser and also has a powerful sniper scope. It also shows up, carried by both Maverick and Paz, in the last episode during their covert mission.
Here's the odd man out: in 'On Both Your Houses', Maverick, Archer and Maniac jump out of their fighters and draw these weapons... and then later in the episode they're carrying the square 'Navy sidearm' seen above. These could be the marine sidearms mentioned earlier in this post.
So... next, lets look at the Kilrathi weapons from Academy, and then maybe the movie guns?