This may make sense to you, or it may not. I haven't seen the original New York Sun article it was published under, but several papers in November 1886 reprinted a Sun story under the title "Yarns About Sharks: The Old Sailor Is Of The Opinion That Not A Few Of Them Are Untrustworthy".

The whole thing is rather dialectical and filled with jargon (with which I'm not familiar), which impedes my understanding, but the implication to me of the following quote is that Shenandoah may be a tune to a task after the capstan is down?

"... Then we got the end of a spare coil of manila, fit for tops'l halliards aft, turned a runnin' bowline into the end on it, slipped the noose down over the line, and then over the shark's nose by workin' him alongside, and so got the noose around the small of his back, which its where his tail sprouts. T'other end we leads to a tail block in the lee foreriggin', takes it to the capstan', and walks around to the tune of 'Bound away o'er the rollin' river,' which all the men could sing beautiful."(via The Boston Globe, Nov. 7 1886, p. 17)