My opinion is you will lose all benefits of either tool and gain nothing in the end. Hawks are hawks, light, packable, easy to repair, ok choppers. Hatchets are sturdier, better choppers, splitters, and capable of bigger tasks. They can be considered interchangeable, but to try and make one from another is ging to result in a chimera.
If you were tempted to do it properly, I would go this route: forge the cheeks down and draw the edge out. Drift the eye to a hawk shape and using a fullering tool pinch the poll and draw it out. Hot cut the poll off a bit to maintain proportions.
if you are looking for an inexpensive 'hawk, get a piece of used car leaf spring and forge it out to a fan shape on one end and to a point on the other. burn it through a piece of maple or hickory, glue, tie, pin or secure it however you want. Search for some projects on here by member Pipeman.
you can also grind down a piece of leaf spring to the shape you want for this method, but start with a 1/4" thick piece atleast.
-Xander