Only those without a swim speed have disadvantage on all their rolls to attack while underwater. With the exception for if they use daggers, spears, crossbows and a few other weapons.
A creature, regardless of type, with swim speed, does not incur disadvantage while fighting underwater with a sword, for example. And even if Zahn were to explore an underwater tunnel-cave, he would not have disadvantage in a fight due to being blind owing to a lack of light: he has a moontouched longsword. It sheds magical light, so as long as an opponent closes into melee with him, he'll be able to aim his swings and hit reliably.