So, as was common in the Civil War, it's starting to look like this song drifted from person to person and side to side and changed a bit with their personal vantage points. I found here a reference to a song called "Lincoln Was a Union Man" by Dee Hicks, from the album Five Miles Out of Town: Traditional Music from the Cumberland Plateau. The lyrics from there were:

Honor boys, honor, honor don’t you know
War is ragin’, you’re all a-bound to go
I’d rather be a Union man and carry a wooden gun
Than to be a Rebel and always have to run

Unfortunately, I can't find Hicks' recording online, but I found a cover of it from the folks over at banjohangout. I'll transcribe the lyrics and add them in a separate post, but from listening to the recording, you can tell it's the same rhythm.