I like the Dead Man's Hand sets for what they are, but they really do have a chunky, doughy look to them, and are a bit short compared to WA's figures, I think - Dead Man's Hand figures compare closely to Oathmark, Frostgrave, and Stargrave figures. If you can live with that, I'm sure they'll be great for that sort of thing! Speaking of Frostgrave, the "Ghost Archipeligo Tribals" kit is definitely rooted more in pulp fantasy than any real-world native tribes (they don't seem to have left the Stone Age, either!), but can surely pass with a little imagination for native tribesmen from the Americas, Pacific Islands, Southeast Asia, Africa, lost continents, the Hollow Earth, Victorian Mars or Venus, and elsewhere.
The Perry ACW stuff looks to me like it would absolutely be close enough for at least pulp Western cavalry, and could very likely pass for Americans in the Philippines, Cuba, China, and elsewhere in the general "Gunboat Diplomacy" era. I'd have never thought of using them for British lancers though - what a great idea!
I'm pretty sure there are at least a couple hard plastic kits out there for Native Americans - I don't recall if they were Plains tribes specifically - I seem to recall one might have been, and another might have been for Mohawks or similar tribes - but if you've got do make do with what you've got, you can do worse than to use the wrong tribes for stand-ins.
I'm all for Wargames Atlantic expanding into sets of "cowboys and injuns", frontiersmen, banditos and desperados, and so on for the Imperial Conquests range! It was a pretty busy period of history with lots of interesting history, geopolitics, and military adventuring going on, and the Wild West is surely a popular enough genre to work with....