Do you have a cardboard box large enough that the sides of the box would cover the ax. If so cut the cardboard to fit the ax(in a square or oblong shape)....you could piece the cardboard pieces together where they would be flat on the ax...then use tape (duct tape works good) to tape the 2 pieces (top & bottom) around the ax. Of course it Won't be real flat ......then just use gift wrap to finish it up. Hope that all makes sense.
I have used the above on several odd shaped gifts and the person getting the gift can't figure out what the gift is.
Then if that doesn't work for you.....there is always the Big gift bags.....but I am Not sure they would work real good for an ax.
Hope that helped.