Even though not (yet) explicitly stated, I think there's little doubt Jack has fishmen genes. Same thing for his DF; it's not explicitly said it's a regular one, but the way they were talking about it, makes it pretty certain. And even if it was artificial, it's certain that Jack is completely immobile at the bottom of the sea, so it being artificial or not is actually not relevant in this case.
DF on itself don't drown someone, they make the eater a hammer in water, which will lead to drowning as he can't swim, unless of course you can breath under water. And who an breath under water? Fishmen.
Mammoths don't have teeth like that and even though it's not impossible for a human to have such teeth, they are rather characteristic for a fishman.