The 5e Fighter works pretty well were representing your standard warrior types from any of the cultures, though the Eldritch Knight will be out as an option. Maybe Adventure in Middle Earth's Weapons Master might be an archetype option.
The AiME Wanderer class can represent the historical units known as Rangers, but also the general wilderness scout type. The Hunter of Shadows Archetype is out, but the much maligned Beast Master archetype of the 5e Ranger will work. I might also replace Trackless Step with the Ranger's Land's Stride, but this isn't a big issue. Interesting historical tidbit: the terms for skilled firearms marksmen: "crack shot" and "sharp shooter" (the latter a calque from German) are both attested to from only the 1790s.
|art by Tim Truman|
Though the name is borrowed from the Adventures of Middle-Earth class, I think 5e's Barbarian works better. This will represent the fierce, rustic warrior, including some Native American warriors, but also some of the frontiersmen or proto-Mountain Men with which they contended. Weapons would be similar for both: muskets, tomahawks/hand axes, and knives, though some Natives might still employ the bow.