I went to a house concert once, and the singer there had learned this version from a sailor who was 90 years old. The old sailor sang this:

Away, I'm bound away
across this wide world of mis'ry.

I think misery makes more sense than Missouri, because if the singer is from the east (where the Shenandoah River is) and he crosses the Missouri, there are no rivers left where he can ply his trade.