Interesting question. I’ve had an interest in all kinds of martial arts from way back, though I’ve primarily done Japanese martial arts. Unfortunately I’ve never heard of any actual Native American martial arts that were preserved. There are some reconstructed elements, but nothing with direct provenance. Even more than the European martial arts — which had something of a boom in the '90s and early 2000s as enthusiast-scholars reconstructed them — there were huge difficulties in preserving them.
The first problem is that there’s not a whole lot of actual information on North American tribes to begin with. An estimated 90% of the population died out in the decades after contact, and the vast majority of those tribes were never even encountered by Europeans. They died off from diseases and encounters with displaced groups. Even among those groups that managed to survive until fairly late in the game, few ever had any of their histories and customs recorded. The wars in the 1800s that are most commonly thought of are late-stage conflicts, sometimes with mixed groups of disparate peoples. The cultural changes had been already been occurring for 300-400 years by that point.
With the notable exception of a handful of tribes like the Cherokee, none developed or adopted writing, and few outsiders were able to record much detail. In many cases, even their oral histories were lost, and there are some groups we know of only through references from other groups that managed to hang on a bit longer, a bit like the references we have in ancient Greek and Latin texts that refer to works that are no longer extant.
Okichitaw is basically a reconstructed martial art, which is not to say that’s a bad thing. Given a basic weapon form and the human body, there are only so many efficient and effective ways to move. I’ve noticed many, many similarities between very different martial arts around the world.
The European sword and unarmed fighting arts had mostly died out too, with only a few elements remaining like fencing (which is vastly different from its roots), singlestick fighting, and savate. Modern reconstructions of, say, 15th century sword and armored wrestling by people like Christian Tobler and David Lindholm, based on period manuscripts and drawings, are pretty damn impressive and well-developed. If you could throw them in a time machine and have them spar with Talhoffer or Ringeck, there might be some differences in technique, but I’d wager that there were equally large differences between those two sword masters and their parent lineage as taught by Liechtenhauer.
Michael Mann, who is fanatical in his attention to detail, especially when it comes to weapons and fighting in his movies, looked into fighting styles for Last of the Mohicans and found that there basically was nothing historical on how they fought with war clubs and tomahawks, so he improvised with some basic techniques chosen from 18th century European fighting manuals by his fight trainers. You can hear him talking about some of this on the extras for the DVD or blu-ray.
Sports are basically ritualized warfare, and some can provide at least a bit of insight into historical fighting. Lacrosse is from a Native American game that was near-universal among the tribes we know about. (You can see Hawkeye and the others playing it in one scene in Last of the Mohicans.) It’s a bit like hurling, which has also been described as a barely-disguised pitched battle. Hurling makes hockey look like a church picnic, since traps, blocks, and throws using the stick are actually legal contact.
Imagine lacrosse with fewer rules, and no protective equipment, played by people who hunt and kill animals on a regular basis for their food. They know exactly where to strike to cripple or kill and have intimate familiarity with doing so, and their favorite game is a close analog to close-quarters battle with the kinds of weapons they’d use once closer than bow- (or later) rifle-shot. Pretty damn scary, if you ask me.
