If the edge is just a bit blunt then you can try stropping, either on leather loaded with CrO, or sandpaper that you can hang freely (heavy backing). However if the edge is damaged, which is often the case if you have been throwing it around, you will need to hone the damage out. For throwing hawks I would let the edge get pretty heavily damaged before I would restore it, depending on the skill of the user as if you take out every ding you quickly won't have a tomahawk left.
The first thing to do before you start honing is to try and get some of the metal along the edge back into place, this will minimize the amount that needs to be removed during the sharpening. You can try to "steel" the edge by just pushing against the metal that has been squashed with something hard like the spine of another knife. If this doesn't work take a small hammer and try to get it aligned using light, repeated taps.
Once this is done take a file and reset the edge, following the curvature. It is not difficult as you might think as you can easily see where you are filing, and you can feel the difference between a stroke that goes along the curvature and one that doesn't. Once the edge is sharp, you will feel a large burr. You can work with a filed edge, but it won't last long if you are chopping, and the edge is filled with bits of metal anyway so you want to clean it up. Take a small hone (1"x4") and use this just like you would a file to smooth out the edge. Start off with something coarse and stop when you are comfortable with the edge that you want.
In regards to edge finish in general. If you are throwing the hawk as your primary use I would not actually go beyond the filing, as the first time it doesn't hit the target the edge will be mangled anyway. If you are chopping get the finish high both to increase performance and edge life. I end with some stropping on CrO after polishing with a 4000 grit waterstone. . If you want some slicing performance leave it a bit coarse like 600 DMT. The more coarse the better it will slice but the quicker it will degrade when chopping, and the more metal you will remove when sharpening.
The above assumes a convex edge bevel. If the bevel is flat then you can still do most of the above, but for the shaping you can use some system provided the angle setting are high enough. For a throwing tomahawk you want a decently obtuse edge so that it doens't get mangled too badly on a throw that misses. I would set the edge from somewhere between 25-35 degrees depending on steel and throwing style as you can hit rocks. If you are chopping wood you can go under half that, for soft woods about a third. For bone you want 15-20 degrees depening on steel type and hardness. For chopping hardened metal you want 20-25 degrees at a minimum, 25+ if you want to do it with a lot of force.
Of course there is power equipment that can do the above very easily, a belt sander and buffer for example.
-Cliff