Some years ago I heard about a study done by the Canadian Ministry of Transportation. They interviewed survivors of light aircraft crashes about what they had with them, what they used and what else they needed.

One of the things I remember was that your tools should be something you can deploy and use with your non-dominant hand because your dominant hand is frequently damaged in a crash. That says to me to skip the axe and have a folding saw with you. I can certainly use a saw in my left hand much better and more safely than any chopping tool.

Caveat: I have not been able to track down the study and I am not certain I remember all the details correctly.

BTW, one conclusion was that they would happily exchange two-thirds of what they had for more water.