Having some experience rehandling my grandfather's Axe as well as other related woodworking shenanigans, I thought I should suggest the "appropriate" wood to make Axe handles from.
Currently the Axe requires oak, which is known to be a very sturdy, hard wood (which I think was the idea for the axe), but in practice oak is very difficult to shape as well as being very inflexible due to its hardness, which is why it's rarely used in tools, especially high impact tools.
The conventional wisdom passed down by the true woodsmen of the land for generations is to use hickory (not in game ;c) or ash (an ingame wood!). These woods traditionally have very straight grain patterns as well as high durability and flexibility, which make them perfect for axe handles, and in a more modern context, baseball bats.
Anyways, that's my small critique of an otherwise insignificant detail. Take this information as you wish.