Over the past few years, I've modified a number of modern hatchet and axe heads to earlier shapes. Some I did by just grinding them on the bench grinder (cooling them often to retain the original temper). Some I cut up with my chop saw (metal cutting saw). And some I reshaped/forged/tempered in my forge. It's all a matter of what you want to end up with, and what you have to do to the original axe/hatchet head to get to that shape.
I often cut a modern single bit axe head or small hatchet head into two pieces - 1/3 and 2/3. I do this with the chop saw, but the hard part is holding/clamping it down to cut it safely. I usually then cut off the extra metal on the Poll, if I want to round out the eye. The forge then really helps to re-shape the eye, blade, and poll sections. But I also do that with the grinder - if the shape is close enough. If you are forging it, you have to re-temper it. If you are grinding to shape, cool it often to retain that original heat-treat. Just grind off the extra metal that isn't in the right place. Yes, I also use a hand-held angle grinder for a bunch of this, and for that finish work - with both grinding and sanding wheels.
Filing to change the shape will take a long long time. The bench grinder of hand-held angle grinder really speads that up. 2/3's of a modern hatchet head does make up into a pretty good small "bag axe" or belt axe. The other 1/3 forges up into a very good spike hawk - in a much more correct small size. 1/3 of that modern single bit axe head forges up into a good large spike hawk or bording axe (the pole becomes the blade, with the old blade portion being forged into the spike). The other 2/3's can be ground into a good small or "half" axe. If you remove the extra metal on the poll and round the eye, you can get a good classic trade axe, but you have to re-forge it.
The hard part of making any axe or hawk is getting that eye made. Starting with a modern hatchet or axe solves that, plus you already have good metal to start with. The rest is just getting creative, and "seeing" what you want within the shape you start with. A forge to re-shape things really helps, but you can do a lot with the metal cutters and grinders.
Have fun. Just look at the pictures of the original axes and hawks, choose what style/shape you want, and then "see" what can be done to get that style/shape out of that modern axe or hatchet.
Just my humble thoughts to share.
Mike Ameling