Not historian but materials scientist.

I am picturing the jawbone affixed to the end of a stick, but maybe there are better ways.

Human bone has very poor properties for making bladed weapons. The outside of mammal bones is comparatively hard, but still not hard enough to make a particularly menacing blade. Moreover, bone is very porous on the inside. If you remove more than a few mm to sharpen it you will reach the interior which is almost spongy and not threatening at all. While it is true that historically bones have been made into knives, needles, arrowheads, spearheads, and awls, bone does not do well for making anything much bigger than a pocket knife and seems to be reserved for points instead. It is also not hard enough to hold an edge for very long.

But what about bludgeoning weapons? Well, bone has basically no redeeming qualities here either. First, it is very light, lighter than virtually any stone and only a bit denser than most hardwoods. The jaw particularly is poor for bludgeoning since it has rather little mass. Bone is also not very stiff (scientific definition of stiffness being how much something compresses compared to the pressure put on it), meaning it will not do too much damage when it hits something. The jawbone would compress as much as, for example, a skull, which is kind of disappointing; the skull will do as much damage to your weapon as vise versa.

Potentially one could also sharpen the ends of the jaw (condylar process) where it attaches to the skull and use it as some sort of two-pronged stabbing weapon gripped by the chin, but I'm not sure how this would have any distinct advantages over other stabbing weapons.

From an engineering standpoint I don't think a human mandible would make for a very good weapon, which explains why rather few jaw-based weapons have been unearthed around the world.

I cannot answer questions about using a real jawbone as a weapon, but I can point out some more details about the myth of Maui, including the fact that he is supposed to have used his grandmother's jawbone as a hook to fish up the North Island of New Zealand while sitting in his canoe, also known as the South Island. Here are some more details: "There are numerous Polynesian legends of Māui fishing up new land, with Te Ika a Maui (the North Island of New Zealand) the largest. Disliked by his four older brothers, Māui would be left behind when they went fishing. So one night, he secretly made a fishhook from a magical ancestral jawbone and crept into his brothers' canoe and hid under the floorboards. It wasn't until the brothers were far out of sight of land, and they had filled the bottom of their canoe with fish that Maui jumped up, took out his magic fishhook and threw it over the side reciting magic incantations. The hook went deeper into the sea until Māui felt the hook had touched something. He tugged gently and far below the hook caught and together with his brothers brought the fish to the surface." Source So I'm pretty confident that it was supposed to be a magically-endowed jawbone, and apparently a gigantic one, which represented a connection with his elders/ancestors. I reccomend anyone who has the opportunity to do so visit the Wellington Museum of City and Sea, where you can watch a very cool short video presentation on Maui and his magic jawbone. I tried to find a version online, but it does not seem to exist.

The Jawbone has a somewhat significant place in Maori culture, for example, fallen warrior's jawbones were collected after they died in battle (The River Kauaeranga on the North Island name literally means stack of jawbones). In addition to this, Maui was also a fisherman, (he fished up the North Island of New Zealand), and a jawbone is shaped like a fishhook, so the choice of a jawbone as his weapon and tool makes sense both in the jawbone's significance, and it's shape.