Here's a clear map of the Ohio River with the states labelled.
not near New Orleans

[Funny how they don't label the states on the SOUTH bank of the Ohio.
Too banjo-ridden, maybe?]

Throughout this discussion, bear in mind that these rivers used to be much wider and much slower than they are today. Today's rivers have been engineered to handle big boats, mostly barges.

As you can see, the Ohio starts at Pennsylvania's western border and ends at the southern tip of Illinois, where it joins the Mississippi. (Where Huck and Jim got lost in the fog.) For other information, see Sandy Paton's post from May, 1999.

Shawnee was in Illinoi where the Wabash River comes in from the north.    The boatmen in our song are taking whiskey and wheat from Pennsylvania and Ohio to Shawnee and will take rock salt from Shawnee back upriver. So New Orleans, the Natchez Trace and the Mississippi don't come into this journey. Our boatman will get to see his wife in Louisville, but not the other one.

It never seems to occur to these guys that their various "wives" could have had various "husbands", depending on who's in town and who's slogging their way back north. Must have been complicated.

Given how hard it was to go back upstream, it makes sense to have shorter journeys such as this. By the way, I don't think there were many beaches, because if there had been, they would have been using draft animals, not humans, to go upstream.

Oddly, the actual Wabash Cannonball, the train takes good hoboes to Heaven, didn't run near the Wabash River. And that reminds me:

   Oh the moonlight's fair tonight along the Wabash.
   Through the fields there comes the breath of new-mown hay.
   Through the sycamores the candle lights are gleaming
   on the banks of the Wabash, far away.