This pushes the origin back a few years:

From Etchings of a Whaling Cruise: With Notes of a Sojourn on the Island of Zanzibar… by John Ross Browne (New York: Harper & Brothers, 1846), page 18:

“Big-foot Jack, Chaw-o’-tobacco Jim, Handsome Tom, Red Sandy, and the rest of our jolly friends, then seated themselves and called for cigars. Captain Bill Salt told us to do likewise; and, taking out his pipe, he soon enveloped himself in a comfortable cloud of smoke. Without waiting for the ceremony of an invitation, he gave vent to the following ditty, a copy of which I afterward procured from him:

“‘PARTING MOMENTS.

“‘Farewell, my lovely Nancy,
Ten thousand times adjeu!
I'm agoing for to cross the ocean
In sarch of something new.
Come, change a ring wid me, my dear,
Come, change a ring wid me;
And that will be my fond toaken
When I am on the sea—
When I am on the sea,
And you don't know where I be.

“‘Now one fond kiss, my Nancy dear,
Now one fond kiss for me,
Before I go for to begin
To roam upon the sea.
And hear this secret of my heart:
Wid the best of my good-will,
Be where it may, this poor body,
Is yourn, sweet Nancy, still—
Is yourn, sweet Nancy, still,
Wid the best of my good-will.’

“This song elicited the most rapturous applause. Captain Bill then spun us some tough yarns….”