Well... I do a bit of trapping here where I live. Day trip stuff. If these knives have to do everything, I guess this is what I would bring.
An Old Hickory 7" butchers blade. This would be used largely for food preparation but the nice upsweep at the tip would be great for skinning and fleshing beaver. Not to mention butchering any big game that may be taken. Nice size handle for ease of use both in the cold and in the warmth of my cabin. A quick touch up with a file or easy yo get razor sharp with a stone,I am well impressed with mine. And when I drop it in the snow and never see it again, it doesn't break the bank or the heart.
A full sized stockman. 4-4.25". This would handle most of my pelting duties along with general use. Carbon steel easy to get sharp and keeps an edge for when the line is good to me. 3 blades gives versatility for when different shapes make some cuts easier, both pelting and whittling.
Some sort of scout style knife with a bail. A blade for utility, awl for bush repairs, saw for bush repairs and a can opener for my beans. Dummy corded to me because you can let it hang while working on the line.
As for other traditional gear,I would suggest, in no order of importance, snowshoes, a billy can, rope, full sized axe along with a rigging hatchet, fire kit, pliers, hand drill, tin cup, cast iron dutch oven, appropriate outer wear, wire, various sized oil cloth sacks, saw, shovel, bucket... I could go on. Pack that canoe full!