I suspect it's going to be hard to get definitive research on Native American, African, and Oceanic blades, because so much of these civilizations were broken up and destroyed by interloping during European expansion. Since so much of these cultures were still small in population, and those populations were mostly loosely networked tribes with no written language, there isn't much to go on. Considering that mystic beliefs were very strong amongst so many of these cultures, including the imbuement of power within objects through craft and ceremony, it stands to reason that something like a legendary blade of some kind might have existed, especially among particularly martial or hunter/gatherer societies. Of course, again, if the oral tradition is lost, and so much of it is, then you might be out of luck.
It might help you to research specific civilizations within Africa and the Americas, and the myths/artifacts that are known about them. In North America, you have the Adena, Hopewell, and Mississippian civilizations in the East; you have the Haida, Tlingit, Kwakiutl, and Inuit in the Northwest; you have the Anasazi, Hohokam, and Mogollon in the Southwest. I know that there are artifacts that show incredible organization amongst the Eastern civilizations, and there are finely crafted metal artifacts, which might have led to metal bladed weapons. The Haida and Tlingit were at least knowledgeable in copper working. Whether they progressed beyond copper, or forged metal weapons, I'm not expert enough to say.
In Central/South America, there are the Inca, Maya, and Aztec, at least that's as fare as my knowledge goes.
As far as Africa goes, there was, of course, the Egyptians, and other Nubian civilizations. However, I couldn't tell you too much about many others, so I Googled it, and found this: http://wsu.edu/~dee/CIVAFRCA/CONTENTS.HTM
Perhaps it can provide you some leads to myths or stories involving great weapons.
That's all I got for now. I hope it might help, at least as a kicking-off point.