To start with Shenandoah was a shanty, a work song, so there's a rhythym in it all right, reflecting the needs of the work it was helping with.
It was probably primarily a rowing song, so if you think of the rhythym of rowing you've got it. But the rhythym of rowing isn't like that of walking, left-right-left-right, it's more spasmodic, with pauses and all that. Write that down in conventional musical notation and I suppose it might get a bit complicated.
That doesn't mean that it's wrong to sing it other ways, if that's how your fancy takes you.