Draw the profile of your chosen ax on cardboard. Use a weapon's encyclopedia, or search for images online to find a suitable ax. Choose one that makes sense for the character who is carrying it for a more believable prop. Cut out two of these straight profiles out with a craft knife, and brush a coat of white school glue onto the face of one. Lay them face to face, and use books to weight them down until the glue dries.
Cut two more profiles of the handle, 1/4 inch narrower than the original. Cut a second pair, 1/4 inch narrower than that and paste the four pieces, two on each face of the ax handle, with the widest pieces centered on the original handle and the smallest centered on those. Wrap masking tape around the handle at the top, bottom and middle to hold them in place.
Cut out three pairs of profiles for the head of the ax. Cut each one with the curved end of the blade 1/4 inch shorter, from the back of the ax head to the blade edge, than the last, but with the head the same from top to bottom. Glue three of these, largest to smallest, to the sides of the ax head and tape them in place. Allow the glue to dry three or four hours.
Wrap the handle and head with duct tape, wrapping from the back edge of the ax to the front. To create a smoother profile, wrap at least two layers around the entire ax. Spray paint the handle brown the head silver, or leave the entire ax unpainted.