There are quite a few examples of hickory arrow shafts in museums made from split or riven wood. If you can get your hands on some 4x4 or larger chunks of straight grain hickory you can split it out in 1/2 inch thick slabs, then split the 1/2 inch slabs into 1/2 inch squares. Once you have the square stock split try your hand at heat straightening the worst of the curves out. Once you have fairly straight squares, you use a small handplane to shave off the square corners to make octagons, then shave off the corners of the octagons to make a 16-a-gon (or whatever that is called). At that point, using 100 grit sandpaper you can get them pretty near perfect rounds...voila! Arrow shafts.
If you are ornery enough, you can do all that using stone and bone tools like those that went before us. If they can do it, we can do it.