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Ash and hickory is the only two woods you should consider.
Oak is hard and durable, but it's not impact proof and it WILL splinter and pinch your hands. Birch is too soft.
If it's for casual outings with maybe 4-5 minutes of use each trip, you can use whatever the heck you want.
If it's for hardcore tree murder you should pick ash or hickory. Also wax and clearcoat on the shaft(...) will give you blisters, oil won't.