I'd either re-shape the eye to repair the head in my forge (if it was a really good quality head) which would also require re-heat treating the head. You might be able to cold-forge it back to a more reasonable and workable shape, if it is differentially heat treated (a gentle etch will identify whether or not there is a visible temper line). Failing that, I'd dismantle the thing and throw it out so that I never run the risk of taking someone's head off at a particularly inopportune moment...
Axes are about the most dangerous outdoors tool there is at the best of times - no sense in taking a punt that it will hold together under heavy use. I'd be worried about the head loosening and deflecting suddenly on impact, sending your stroke off at an angle, or the head simply flying randomly off to do what it will, or...
Makes me shudder