If you were to have the hawk made it would still need to have a short tang to attach it to the handle...similar to the newer SOG hawks like the fasthawk. there is the head then there is a short 3-4" shaft where a metal ring is used to lock the head in place on the split handle. It also protects the handle in the join area from over strikes. Hell, ask Winkler if he can make you one.
I'd prefer to have a drifted eye and appropriate haft, actually. Or maybe something like Edwood posted, but a composite handle, of course.
Hmm... what about a Warren Thomas Ti head with carbide edge... It might not be practical, but it makes me salivate.
And my wallet just exploded. Poor little guy couldn't even handle the thought of a custom titanium hawk head. Didn't stand a chance.