Like Tom Sawyer I like the flat-sided hatchet except mine is a broadaxe. These really do the trick. I get my bow pretty close with the broadaxe and can chase a ring with one if the rings are not too close.
I reduce my fresh cut staves to near bow dimensions (well, width anyway and leave an extra half to 3/4" on thickness) right away for faster seasoning and to take up less room. On osage I always remove all sapwood. I make chops in the sapwood on the sides of the outer surface so I can watch how deep I'm chopping, then take chops across the middle to match. Then with the broadaxe I can take off about all the sapwood in a hurry to the right depth, till i begin to see color peaking through. Then I get the drawknife.
I never had luck removing sapwood on black locust before seasoning, so i don't anymore. Removing it with the broadaxe is hard work when it's seasoned.