Connecting to small clock battery terminals
I would go to the store and purchase a wood dowel that is the same diameter as the AG13 battery. Then you can craft up a small pellet that has some small holes drilled at appropriate places and angles to insert small wires from your wire harness. The best termination of the wires would be to acquire some copper tape that has conductive adhesive and apply a couple of small pieces to the dowel side and face to mate with the contacts in the clock.

Do note that the wood dowel piece does not need to be as thin as the AG13 battery. It could be longer and even protrude some out from the back of the clock. 

If you do not feel so much up to the task of DIY craftsmanship then I would suggest that you can just solder your wires directly to the contacts. This type of clock module is not so precious that you need to find a non-destructive manner to connect the wires.