The Leavenworth [Kans.] Times (Oct. 10, 1905) gives another text and connects the song with Civil War:

"Some of the old boys tried to sing an old 'catchy' tune, [which was] invariably started up by a regiment, when starting out on a march in the morning, going to the front, and passing by the regiment in front of them, who were to take the rear that day....[W]e publish the words, but for the music, the disputants must decide for themselves:

"There was an old soldier and he had a wooden leg;
No tobakky could he borrer nor tobakky could he beg.
There was an old sailor as cunnin' as a fox,-
He always had tobakky in his old tobakky box.
Says the first old cod: "Will you gimme a chew?'
Said the second old cod: 'I'll be dinged if I do!
Save up your money, be as cunnin' as a fox,
And you'll always have tobakky in your old tobakky box!"

"Cod" = fool.