This is likely a coincidence. The quoted source is a Victorian book by a trance medium - written at a time when spiritualists and mediums were the rage:

Cora L V. Hatch, "Discourses on Religion, Morals, Philosophy, and Metaphysics" (N.Y.: B. F. Hatch, 1858), I, 372:

“ 'Shenandoah’ is the name of an Indian maiden, who frequently controls Mrs. Hatch; and the reply was written while Mrs. H. was entranced.”

Maybe Mrs. Hatch was inspired by hearing, somehow, the matching verse of the chantey. Outside of the writings of Mrs. Hatch (who seems to have written of her Shenandoah for more than a decade, I find no 19th century example of "Shenandoah" as an "Indian maiden" and in close proximity to the phrase.

P.S.: Surely the line, "Oh, Shenandoah, I long to see you!" referred to the maiden and not her father!