Here is the camp axe I was talking about:
http://www.lowes.com/lowes/lkn?action=productDetail&productId=147585-302-1116400&lpage=none
Even though it needs some work, it has a good basic design--strong thick handle of the right length and contour, a 1 1/4 lb head, well-balanced between handle and head, decent steel temper for obtaining and retaining good edge, and contoured fairly well for thinning the edge (for cutting) and retaining the thick eye section for splitting. I have one I reworked (thinned the first 1" of the bit, blued this steel for 1", epoxied the top of the eye, oil finished the handle, waxed the works) and with a waxed leather belt sheath I had in stock that fit, I would happily take to the trail with it. The products and tools I had on hand, so my expense was minimal to have a good camp axe.
Also keep in mind that a hawk is really better for lifting scalps, self-defense, and throwing, than cutting and splitting wood. The hawk was developed as a compromise between a weapon and a tool. I would think in a survival situation you would want to err to the tool side, as there are not that many Injuns or Redcoats left in the woods. The cutting edge of a hawk will often tend to flip around in your hand while felling (unless there is a hammer poll)and the eye of the bit at the handle on many hawks is often too abruptly widened for good splitting. In shaving or carving the nearly round handle is harder to keep from turning in the hand. One advantage of the hawk is that a straight tapered handle is the easiest one to replace in the woods should it break.
In a survival situation, having the ability to cut and split wood for a fire is essential. The axe will also be used to fashion any instruments you need from wood. IMO a traditional wood/steel camp axe is preferable to the other options.
As a survival tool which may see a lot of abuse I can understand not wanting to shell out the dough for Gransfors Bruks. So you can go with a "cheap axe" as mentioned above which will require some work to make it trail-worthy or step up to a Wetterling or Vaughn which is more expensive but requires minimal work.
It takes either some time and work or money to have a good camp axe. There is no free lunch for a survival tool.