I just love hypothetical speculation! Many people hate and despise it, but to me it is nearly always interesting.
Well, anyway my first thought was I would like to dispense with the sleeping pad and replace it with a hammock or a tent. However, like the majority of you, I was drawn to the cutting tool dilemma. What to take? My first thought was not unlike Hoodoo's in that I cannot imagine why anyone would want an axe. They weigh a ton (after a few miles), and I wouldn't use it anyway. As a builder of at least a thousand campfires, I assure you I have never split a single large piece of wood to build one. split some small kindling, yes. True a knife is a bit tedious even for this small chore but I'm not going to carry an axe to overcome this minor drawback.
I have an EnZo trapper, and that was what immediately sprang to mind. I do have a kukri and that was a distinct possibility, but I gravitated back to the EnZo. However, after much anguish I have come to the conclusion that BR. Red's Wenger 57 would be the better bet. Not the better knife, but having a good knife with a saw is just too hard to pass up. I was a late comer to folding saws, but have really come to appreciate them. In the real world I would take my EnZo and my Gerber saw. But, in this hypothetical world, I'll take Red's Wegner, if he will loan it to me.
By the way, I love good axes and good hatchets, I split a lot of wood, and I do understand that split wood burns better than unsplit wood. I just never found the need for split wood when out in the woods.