As noted above, lumbermen's songs are fairly easy to find, and Doerflinger is a good available source.

True traditional trappers' songs are very rare, if they exist. I personally know of none at all, apart from the voyageur songs to the extent that they dealt with trapping (not much). They were solitaries and I'm guessing they didn't sing while setting traplines if only not to scare away the beaver, marten, etc. they were trying to catch. As far as I know their only social moments, when music might have been a possibility, were the times they wagoned or backpacked or sledged or travoised their hides to market at trailhead forts or in cities like Montreal, Chicago, etc.

Voyageur songs, tales and history are not easy to find. But I was lucky to run across this excellent trade paperback, which I recommend:

Grace Lee Nute, THE VOYAGEUR, reprint ed., Minnesota Historical Society, St. Paul, 1955, paperback ed 1987. It was first pub in 1931 by D. Appleton & Co. The contents: chapters on

Furs and Fur Traders,
Portrait of the Voyageur
The Voyageur's Canoe
Voyaging
Fort Life
Voyageur Songs
The Voyageur As Soldier
The Voyageur As Settler
The Voyageur As Explorer

The Voyageur songs included, and songs sung by the voyageurs from earlier French tradition, in some cases with music, and English translations added, are as follows. Note that few of them are about voyaging! But that's similar to lumberjacks -- they sang abundantly and only part of their songs were about the lumber camps and lumbering itself.

A La Claire Fontaine
J'ai Trop Grand' Peur des Loups
Voici le Printemps
Frit a L'Huile
La Belle Lisette
Une Perdriole
J'ai Cueilli la Belle Rose
Quand J'etais Chez mon Pere
La Bergere Mouette
En Roulant ma Boule
Nous Etions Trois Capitaines
Ah! Si Mon Moine Voulait Danser
La Belle Francoise
C'est Dans la Ville de Bytown
Parmi Les Voyageurs
Salut a Mon Pays
Le Retour du Mari Soldat
Petit Rocher
Quant un Chretien se Determine a Voyager

I'll save further comments for a second message. Bob