Hi, Steve.

Ordinary Seaman Frank Townshend, described as an "Irish fiddler and wit," wrote a poem on the fight between his ship and USS Hatteras.

The poem was set to a variant of the tune "Brennan on the Moore" not long ago by Dan Milner, Frank Coffin, and the fortuitously named Jeff Davis:

https://www.youtube.com/watch?v=ZF3swX6kv_A

They also perform the parlor song "The Alabama," by E. King and F. W. Rosier (1864):

https://www.youtube.com/watch?v=zw-QY5s4FHs

And R. B. Nicol's 1864 broadside "The Fate of the Pirate Alabama":

https://www.youtube.com/watch?v=F7lFv50E-Ec

The 97th Regimental String Band has recorded Frank Wilder's "Alabama and Kearsarge" (1864):

https://www.youtube.com/watch?v=Lmp4DLzHveI

I don't detect any real similarities between any of these songs and the chantey. Unfortunately.