I have another verse. I must have learned it from Lynn Hardy at the Middletown (NJ) back about 1978. I don't know how trustworthy my memory is but I've enjoyed the song for years.

Travelled the world and I'm all through with it
No more will I roam.
Burned my home, what can I do with it?
I can't live all alone.
No use wasting time
I just know that I am ready


I'm ready for that river, that shivery river
Get that river ready for me
I'm gonna drown my troubles, there will be just some bubbles,
To indicate what used to be me.

I can't swim, neither can I float
I got a lot of lead pipe in my overcoat
I'm ready for that river, that shivery river
River that leads down to the sea, the sea
River that leads down to the sea.

Ain't no used to try and slow me down
I can't stay, no I just can't stay
I had a gal and I had her through me down
She's gone away
It was solitude that put me in this mood

I'm ready for that river, that shivery river
Get that river ready for me
I'm gonna drown my troubles, there will be just some bubbles,
To indicate what used to be me.

I made my will, I wrote some notes
I'm gonna keep walking till my straw hat floats
I'm ready for that river, that shivery river
River that leads down to the sea, the sea
River that leads down to the sea.