There is nothing wrong with a fighting hawk with a wooden haft. There are better choices, but full tang, IMO, is not one of them. That much steel will just slow you down. More mass means more inertia. Recovery from a strike being potentially ultimately important in a fight, you want as little mass as you can manage without sacrificing durability or power. That means taking it out of the handle, because mass in the head is what gives it the power. You will also want a decent trailing mass to aid in tracking and direction change.
From the tops line, I would choose the IDT, if the weight distribution is alright. I suspect that it's not, but I don't know enough about the chrome moly tube they're using. It's also a little short at 15", but I like the head shape. Next up would be the ECO Hawk and make a handle yourself, out of wood or something else if you've got the skills or connections to do it
To fight, I wouldn't go shorter than 18", 24" optimally for me. Your preference may be different. If you go with a wood handle, I'd recommend starting at about 30" and working your way down in 2" increments (hand placement, not cutting) until you're comfortable. Remember, you can always cut off excess lenght, but you can't add to it.
By odd shaped, are you referring to the Winkler/Sayoc RnD hawk? If you've got the scratch, go for it. If you don't like it they seem to hold value very well.