What would surprise us about the vernacular of the common Tennessean or South Carolinian in the early 1800's? What expressions were used profanely that would seem mild or strange today? Given the lack of education and maybe sparse communities did these people use cuss and swear words similar to today's frequency?
It's difficult to know exactly how people spoke in earlier times. Also, when asking this question, it is important to know which class of individuals you are speaking of. "Upper crust" used language differently than the "common" person. Also, swearing is a highly individual matter.
One reason this is a difficult question to address is that the printed word was kept to certain standards of "decency." However, the long history of censorship clearly shows that people wanted to express themselves in print in ways not accepted by authorities (government, post office [Comstock], religion, literary standards, etc.) So, in my opinion, trying to look to Google Ngrams for hints at swearing only shows trends in censorship. To look at books for examples of swearing is the wrong direction. Was the F word used just as much in 1800 as it is today? I don't think we will ever know. Some say "yes" assuming that people were just as vulgar in "the good ole' days." I don't think so.
There is the expression "To cuss like a sailor" which clearly indicates that sailors used "colorful language" to express themselves. There is also the expression "take the lord's name in vain" which seems to indicate that at one time when swearing people said "God dammit." or the words "God-damned." People still do, but I think it has less shock value now than in 1800.
People have always used race, religion, ethnicity, sexual interests, level of intelligence, or place of origin to insult another person, along with references to body parts. It was no different in 1800s America. A quick search under "swearing in victorian times" reveals numerous websites hosting articles about the subject. The words may change (and you can look them up yourself) but the idea is always the same. Many of these words are foreign to us now. Also, I don't we will know them all because swearing can be very specific to a region or profession.
In 1800s we might hear someone say "Roberts, you're a God-damned fool." Compared to modern "standards" this is mild, however in the 1800s the swearing part would have been "God damned," not "fool." If you were a sailor, a reference to someone's birth would do the trick, so calling them a "son of a gun" "bastard" or "whore's son" would be insulting. More so back then, because birth origin was deemed more important than it is in modern times. Although users will most likely disagree about this, calling someone a whore's son in 1800 was legally good enough to challenge someone to a duel to defend their honor. We also might hear someone say that they resemble female or male anatomy...same as we do nowadays.
Insults most likely took the form of questions or statements. So it is possible a person in 1800 could insult someone by asking "Are you sure you are not the son of a whaling captain?" or "I heard the cavalry came to town about the time your mother excused herself from public." or "I hear masters know their servants where you come from." or "You don't look like your father." or "Your mother is quite popular with sailors." Etc. But a quick grab in the insult bag for a vulgarity was certainly done. Calling someone an ass, whore, bootlicker, or clamface was done.
In your question, you mention lack of education. In my opinion, education doesn't really factor in to how much someone swears or whether they swear more than others. People are people. It is common in historical discussions to portray farmers, sailors, soldiers, etc as the swearing types and upper crust as more reserved. I think that's baloney. People are people. Maybe the kinds of insults changed, so an aristocrat might insult with a birth reference and a sailor might reference female or male genitalia but I think swearing was / is equally distributed among the classes.