I heard a secondhand reference once to a Canada Ministry of Transport study where they interviewed pilots who had survived aircraft forced landings. The interviews went through what equipment did they have with them, what did they use, what did they NOT use, what did they need (water was on the top of that list).

One thing they noted was that you should pick tools that can be deployed and used with your non-dominant hand, since that hand is frequently damaged or broken in an accident.

That suggests that a saw would be better than an axe or machete both for cutting and for safety. I fear that the limbs I would cut off using an axe lefthanded would probably be my own.