Let's be clear for most readers: an Indian chief version *could be* the original, but we have *no* way of knowing that. It could just as easily have been a fantasy spun out by a later chanteyman.

In the familiar words that chill the blood of any folksong enthusiast,
"Who knows?"

As for the Oneida chief Skenandoah (who died in 1816, long before the routine singing of chanteys), he was born in Pennsylvania and spent most of his life in western New York State.

That's pretty far from both the ocean and the "wild/wide Missouri."

Finally, Wikipedia cites an assertion that George Washington "named the Shenandoah River" in the chief's honor. In actuality, the river was called "Shannandore" (sic) by 1746.