The earliest appearance of a "full" text of "Shenandoah" may have been in:
The Riverside Magazine for Young People (New York City), April 1868, p 185.

Shanydore


"Man the capstan bars! Old Dave is our 'chanty-man.' Tune up, David!

O, Shanydore, I long to hear you!
Chorus.-- Away, you rollin' river!
O, Shannydore, I long to hear you!
Full Chorus.--Ah ha! I'm bound awAY
On the wild Atlantic!
                                                   
Oh, a Yankee ship came down the river:
Away, you rollin' river!
And who do you think was skipper of her?
Ah ha! I'm bound awAY
On the wild Atlantic!

Oh, Jim-along-Joe was skipper of her:
Away, you rollin' river!
Oh, Jim-along-Joe was skipper of her!
Ah ha! I'm bound awAY
On the wild Atlantic!

An' what do you think she had for cargo?
Away, you rollin' river!
She had rum and sugar, an' monkeys' liver!
Ah ha! I'm bound awAY
On the wild Atlantic!

Then seven year I courted Sally:
Away, you rollin' river!
An' seven more I could not get her
Ah ha! I'm bound awAY
On the wild Atlantic!

Because I was a tarry sailor,
Away, you rollin' river!
For I loved rum, an' chewed terbaccy:
Ah ha! I'm bound awAY
On the wild Atlantic!


"The words to the songs given here were from the lips of a veritable 'old Dave,' during the writer's recent voyage across the Atlantic."