She lives in an underwater kingdom in international waters and can legit swim whever she wants (even though that often upsets King Triton, absolute zaddy [why did you make me type that freeform]
But for the sake of the argument, let's say that Ariel, too, is Danish. Danish mermaids can be black bc Danish *people* can be black. Ariel can sneak up to the surface at any time with her pals Scuttle and the *ahem* Jamaican crab Sebastian (Sorry, Flounder!) and keep that bronze base tight.
Black Danish people, and thus mer-folk, can also *genetically* (!!!) have red hair. But spoiler alert - bring it back to the top - the character of Ariel is a work of fiction.
So, after all this is said and done, and you still cannot get past the idea that choosing the incredible, sensational, highly-talented, gorgeous Halle Baily is anything other than INSPIRED casting that it is because she 'doesn't look like the cartoon one", oh boy, do I have some news for you... about you.