Ok. After hours of deliberation, I have finally discovered how to remove the exterior door handles. I'll divulge the information for future reference. First, remove the door panel. Next, detach all wiring to the locking mechanism. Thirdly, remove the cotter pin from the wire to the exterior door handle (It is at the top of the wire, adjacent to the handle. Kind of hard to get to.). Next, use a flat head screwdriver and lift the 'spring' on the side of the door handle. Use another flathead screwdriver and position in-line with the saw-tooth metal piece. Push really hard to remove the saw-tooth piece. Do the same with the other side. Position the swinging arm on the inside of the handle so that [the handle] can be removed. Pull or push the handle out.
For '97 Jeeps, or any others that have the same 'backwards' door handle problem, remove the wiring that goes from the locking mechanism to the exterior handle and bend it so that the wires are parallel to each other. Place back in and replace the original handle with that of the other door. Place cotter pin and reattach other wiring and you are all set to go.