Only way to get better with an axe is use one mate
With regards to historical accuracy its all just a bit of fun so dont fuss too much as t if boone would of had one.
With modern day restrictions/moral obligations/understanding of good practice a saw is a wiser choice in honesty its not as offensive looking, makes a much neater cut so better for the tree and is easier to pack.
Albus yup man up you'll be fine. Just sleep closer t the fire or consider what else you've got to keep you warm liks a pair of camp moccasins/thermal socks and a wooly hat or even kip in swannie.
The US canteen definitely worked better than a standard one ltr bottle. Water is always something that needs considering and I suspect findi or accessing safe water was a massive influence on where boone went on his travels