Hm... the tattoos are clearly influenced by modern designs, which favors complex designs, even though it uses a lot of arrow and ocean patterns, which is consistent with Hawaiian tattoos.

It isn't traditional, though, I can tell you that much.

Traditional Hawaiian tattoos are simpler and tend to have a consistent repeated pattern of shapes.

Like so:

Jason Momoa, for example, has a traditional Hawaiian tattoo on his left forearm.

However, for King Shark, I can also tell you that the body placement of the tats is wrong.

There's two places where his tats is most likely to be:

1. On his ankles. Ancient Hawaiians used to have arrow patterns on their ankles to indicate that their aumakua was a shark.

After all, Nanaue is the son of Kāmohoaliʻi, who was a shark god. His father was his mother's aumakua (which, they actually got right in Superboy #9), which means that, as her son, his father is also his aumakua.

Which brings me to..

2) Tattoo designs on his torso (that is, chest, back, and stomach). Body placement is not random. Because his father was a god and not a chief or anything of the like, King Shark's tats would also likely be on his torso. One's mana originates from the navel.

Since Hawaiian gods are often considered having much mana, there's a very good chance that King Shark's tattoos would be placed on his stomach, particularly since not only is his father a shark god, but he is a demigod.

King Shark's original design had it much closer to being right, even if it wasn't a tattoo.

If anything, the only thing it likely got wrong was putting one of the bands on his arm.

Tattoos on arms were usually used for those who were warriors or chiefs.

Since neither King Shark or his father was neither of those, that would likely be inappropriately placed.

The thighs make more sense, as its not very far from the navel, and usually tats on the thighs tend to be done with a nod towards family.

Given his father, that's not an inappropriate placement.

At the very least, King Shark's bands have the consistent repetitive pattern down pat.

The whole reason I mention all the stuff about traditional tats, is that canonically, in the DCU (at least post-Crisis King Shark anyway), Nanaue is ancient. Since his legend pre-dates western contact, he's more than two hundred years old.

His tats would be traditional.

I have my own shark man character, and his tats are traditional and likely placed correctly.