Close quarters violence underwater wouldn't be impacted as much as you might think. There are four areas I can think of where they would be adjusted. In general, they are effected by two factors: water resists movement, and shorter range means it's harder to put an AoE attack far enough that it doesn't hurt you.
Hand to hand
Heavy swung weapons like hammers and halberds wouldn't be effective because they would lose too much energy. Blunt trauma weapons like clubs or morning stars wouldn't exist.
The most efficient melee weapons would be spears and knives. You could do some sword-like things, but they would be mostly ineffective against armor. Aerodynamics would be a huge factor, changing the shape of anything swung to have the lowest amount of drag, and it would take more skill to hold the weapon at the right angle.
It occurs to me that you could have a axe-like weapon with a thin profile, but for which the wielder purposely turned the weapon in mid-flight to change its trajectory. Again, you'd want the Myth Busters to actually test the effectiveness of such a thing, and it's doubtful that it would be more effective than a spear.
Fire arms
This is the land of spear guns. There are numerous implementations of pistols and rifles that can get significant range under water. By "significant" I mean "pathetic by air standards." The equivalent of a sniper rifle has an accurate range out to around 60 meters, and your typical rifle will have half that.
The trick is that you use long, pointy projectiles. Darts, really. And then put a larger explosive charge behind it. You can extend the range by giving the bullet a flat or concave nose, which creates a tube of vacuum, eliminating drag along the edges of the bullet. Even then, a bullet will continue moving until it displaces its mass x velocity in water, which makes it a mass-to-cross section formula. By putting more mass behind a smaller cross section, you get significant range improvements.
The underwater equivalent to a gyro-jet wouldn't have adequate accuracy, as small water currents would throw it off. It would be like trying for a long golf putt.
Theoretically, you could have a gun that sets off a shaped charge, concussing everything in a cone in front of it. I don't think I'd be willing to test such a weapon, though.
Explosives
The concussive force of an explosive is, in fact, conveyed more efficiently by water. It's almost impossible to throw a normal grenade far enough to not injure yourself.
Thus, we don't use normal grenades. Instead, we use tiny torpedos. Throwing one of these things like a javelin activates its propeller to send it swimming forth towards the enemy. When the propeller runs out, it explodes.
This is an area where the gyro-jet weapon could be useful. Basically, a tiny rocket-propelled grenade launcher. I'm sure this could be scaled up for anti-armor activities.
Weird stuff
The problem with a super-cavitation weapon like the pistol shrimp uses is that, for less energy, you can fire a projectile. The shrimp only does that because it can't grow its own bullets. This could be the basis of a stunning melee weapon, where you poke it at an enemy and pull a trigger, releasing an elastically retracted clapper.
Flame throwers are a non-starter, but you could try sodium/phosphorus rounds.
Gas attacks, like tear gas (tear fluid, in this case), would have effectiveness based on the wet-suit tech used by the combatants. You could launch serious skin irritants into the water, but the shorter range would mean that it would be harder to limit the area of effect to just your enemies.
Acoustic grenades would come into their own. Something that vibrated the water in such a way that it irritated ear drums in the vicinity would be pretty easy to engineer.