Read The Witchery of Archery by Maurice Thompson for descriptions of bows which white Americans were using just post-Civil War. Basically English style longbows. Not exactly pre-1840, but pretty darn close.
Native Americans didn't decorate with snake skins, but rather with paint and beadwork and feathers. Some tribes built recurves, some didn't. Look at the North American section of Tratitional Archery of Six Continents by Charles Grayson for examples of the wide variety of Native American bows.