Here is what I remember as a child but I'l love to find the entire song.

Goin' to the river, the shivery river
so get the river ready for me.
Gonna' drown my troubles and leave just a bubble
to indicate what used to be me.

Made my will, wrote some notes
gonna keep a walkin' till my straw hat floats.
Swannee River, Old Missouri, Mississippi, Wabash too.
If I had you all around me I'd jump into all of you.