Well I'm actually talking about the opposite.
You can't ( and you shouldn't either) stop the jokes as The Deep because there's gonna be jokes about everyone , absolutely everyone including the serious dark edgy characters as Batman, the Punisher or Wolverine.
The achievement was making possible a serious non-comical depiction of Aquaman. It's not about making the jokes banish...it's about making a version that is not a joke ( that for comic readers was obvious , there's decades and volumes of stories there , but for the broader audiovisual audience was not).
That's why they casted Momoa, the toughest more threatening presence they could find although Karl Drogo/Conan didn't match the classic image of Curry. They looked for the baddest looking motherfucker ( as S.L. Jackson would say) and it worked wonders. This was a case of little to no controversy of race swapping ( well , there's flat earthers in the world, zero controversy is impossible) because most people understood why a change of image was necessary from the bland ass blondie of the comics. I mean, there's people complaining about race swapping in this very page of this very thread ( Namor) , it happens every-single-time and that miraculously barely happened with Momoa.
They sent the message ( and people bought it) : "Dare to laugh at Jason Momo's face if you have balls".
And not only in the visual design of the character and the cast. People crucified the character about the "talking to fish" skill ( because yeah there's an obvious comical part of it) that is present even in DC universe ( Justice League the conversation with Batman) and they changed the narrative: "Do you laugh at talking to fishes? Yeah? Look what talking to fishes achieve".
So in the end it's not about comical representations of Aquaman...it's a about a representation that is not. And here and now it looks easy but it was not...we got to concede that to DC because they made a great character that was FULL of obstacles and they made a great movie , so successful that has pushed Namor out of its classic depiction ( that was a battle that Marvel would have lost...and they knew).