My solution is simple.
Stabbing swords and small slashes.
Rapiers come to mind when we start talking about stabbing swords. Basically they come in many forms but all of them are thrust centeric, some to the point of having no edge and others to a lesser degree.
Anyway rapiers offer excellent hand protection, they also have reach over even cavalry sabers, and are some of the best unarmored fighting weapons as they are fast and agile.
Now don't mistake the weapon for less manly sword as rapier have the same mass just distributed in a different manner. They are longer and thinner and made to thrust quickly while keeping the enemy at bay and offering excellent hand protection.
Also remember that many rapiers were war swords and those tended to be a bit shorter with a more cutting blade because duh.
In reality big telegraphed moves are not really that much of a thing. In reality a sword fight can be as quick as two heart beats.
I highly recommend seeing HEMA (Historical European martial arts) video on YouTube as it would give you an actual idea of how actual fights went.
Small controlled moves, a cut and a retreat. Nobody just raises the swords as high as they can like they are using a hammer. That leaves you open to probably more than enough attacks to kill you.
So even in reality you just jab the opponent or do a small cut and that's it.
So both can be done underwater with little effort, your protagonist is super powerful anyway, and can be very realistic.
On the realism aspect let me tell you a well known technique.
Halfswording. Basically if you are fighting an armored opponent your chances of doing damage with the conventional sword fighting is minimal. So you grip the sword from the middle and thus turning into a dagger and try to get that little sharp edge into a gap.
Sword were also used to be held as a club with the pommel at the top and using the pommel as an improvised warhamer.
Both, and many others, are 100% realistic techniques used in history.
So just say that your MUMA (Merfolk Underwater martial arts) focuses on small cuts and slashes.
Here are general sword advantages that you might like and make you incorporate the sword
- Every part of a sword is a weapon. The pommel the crossguard and grip are all incorporated into actual fighting manuals of history. A spear is great but swords can be more versatile.
- Swords were EDC (every day carry) side arms of the times before pistols. Obvious truth is obvious but even underwater I think trying to carry a spear or pollaxe on your back is troublesome. So while even above water the overall advantage of spears existed. People found it easier to carry a sword.
- Paired with how every part of sword is a weapon a sword is a much more dangerous weapon in CQC. You can manipulate the blade better to defend yourself in tight spaces or from an enemy that just closed the distance. In my opinion when you introduce the underwater fighting element this might make swords more useful as the enemy can just come at you from an unexpected angle and that leaves you less time to react and fight back.
- Armor void swords. So sorry. If you have armor your swords will suffer trying to get through it. That is if it compared to full plate armor or something similar.
Basically I think you can keep the sword even without the magic. But as "Renan" so logically suggested just have the magic be like he said if you magic.
Other than that just add the bits about ease of carry and overall advantages of swords and that the martial art itself helps and voila. You have swords underwater without magic or with little magic as possible.
Personally if I can use magic in the situation even for small stuff I would just bring a box of dagger points, or just nails for maximum cheapness effect, and accelerate my weapon of choice to hit the enemy with enough force to penetrate armor. Rinse and repeat. That would be even cheaper than bullets.
Or I'd make little spiked balls that I will shot and have a couple of them run around in the opponents body for several seconds until the desired effect is achieved.
Or for maximum serious and grimdark stuff just cut their veins from the inside or explode their heart or brain or rupture their lungs directly. I actually use this magic in a world of mine. Wizards there take like 3 second to kill a dozen .
But I digress.