Chances are the Chinese steel is a medium carbon tool steel which is fine for hammers , hot sets and stout hot punches. if you are going to try this you should make a "drift" which fits the eye of the hammer. You insert this into the eye as you are doing the reforge heats so the eye does not collapse or distort. Make sure to take a slooow initial heat so you get the hammer heated evenly throughout it's mass. After forging get a nice even cherry heat on the whole tool and put it in a bucket of lime leaving an inch or so of the end you will be pounding on exposed. This will anneal the eye and working end and leave the ass end a tiny bit tougher so it won't mushroom over as quickly in use. Do any cold shaping you need now. I would still recommend heat treating especially if it is a slender hot punch because under a sledge or power hammer the tool you worked so hard on might bend. When you harden just do the working end of the tool up to about the eye. Temper to a blue color and keep the tool cool when you use it. Works for me.