Now that I have everyone's attention, let me clarify what appears to have been the status of "Shenandoah" during the Civil War.
It's hard to imagine more than a tiny percentage of Civil War soldiers knowing anything about this shanty. Since the lyrics were, so far as we know, not in print till long after the war, the only way anyone could learn the song was from someone who already knew it. Any soldier who had served any length of time as an ocean-going sailor was likely to know a few verses, but the work-related context of a shanty makes it unlikely that even many of these men would, say, start a "Shenandoah" singalong around the campfire. Other soldiers, from maritime areas, undoubtedly picked up the melody and maybe a few words from overhearing it sung at the capstan when a ship was in harbor, and undoubtedly some more well-to-do soldiers had heard it sung on an ocean voyage. Some others may have learned a little from seafaring relatives. There is absolutely no primary evidence that anyone has produced to show that "Shenandoah" in any version was the "common property of all Americans" during the Civil War.
As for the melody, that would have surely stuck in more minds than any of the partly improvised "texts" that sailors were singing. I suppose that if the "makes water" stanza was in existence at the time it may have made the rounds as a "dirty ditty," but the better known it was, the less likely its tune would have been played in front of ladies. So the idea of Virginia troops marching off to war with a band playing "Shenandoah" is, with the possibility of in the inevitable weird exception, just fantasy.
So far as has been discovered, no version the fabulous melody was in print either, under any likely title. Once again, the only source was sailor singing.
As the above examples show, many versions of the song as sung by real 19th century shantymen had inspipid or incoherent lyrics. Theer was in fact no "established" text until collectors began publishing their findings in the 20th century. And as is well known, few shantymen - with the weird exception that somebody will always jump on - seem to have paid any attention to the coherence of a shanty. They sang what they knew or what popped into their heads.
So the likelihood of Civil War soldiers in the main knowing, singing, and loving a modern printed version of "Shenandoah" OR the Sandburg/ Dolph/ Lomax "army" version is as close to zero as you can get. Their loss, of course. And like today, the pop culture of the time was churning out new stuff for them to sing and play, much of it highly sucessful.
The most likely scenario I envision would be something like the following:
"Hey Sam! Silas! Hoss! Come over here! Sailor Jack knows a song!"
"Let's hear it, Sailor Jack!"
"Hell, it ain't much. Here goes, 'Aw, Shanadaw, I love yer daughter!'"
"Who's Shanadaw?" "She got another daughter?"
"Hoe the hell should I know. You want to hear this or not?"
"Sing it!"
"Oh ho, ye rollin' river!"
"What river?"
"I ****** the ****** where she *******!"
(Others dissolve in hysterical laughter, some gigglng, "You're a caution, Jack. I swan! Gotta remember that 'un!" Another mutters "filth!" and walks off.)