Thor, I love the look of the Type C TOW shows on the website. Being short, I wanted a shorter barrel and being unskilled, I opted for the Tennessee Valley Muzzleloader Fusil de Chasse.
I don't know how important it is to you to be period correct. If you are a stickler for detail, get the book suggested and ask some questions of the people here who know. If you can accept close-but-I-love-the-look-of-that-Type-C, then go for it.
It appears that those guns were individually hand made and if you went back in time, you would find guns varying in many details, all considered the same gun. Alternatively, you would find many different guns, all fairly similiar but varying in details and noone cared.
Have Fun! Life is short!
Rusty Musket