The Folk Legacy cd "Adirondack Songs and Ballads" sung by Lawrence Older not only has songs about logging (eg Once More A-Lumbering Go), but songs sung in the lumbering camps (suitable for all ages).It's also a treat to listen to.
Just where will you be doing this program? Would it matter if the song was geographically specific? (I'm thinking Blue Mountain Lake)
some songs like the Jam on Gerry's Rocks have apparently traveled around a bit.
And you might want to check to see if your library has William Doerflinger's book Songs of the Sailor and Lumberman. Good luck.