Today I've soldered the first prototype of the key fob:
Please forgive the very raw prototype. As 1-wire device I've used the DS2401 which provides the ID only (as opposed to my earlier test where I used an EEPROM), because it is the cheapest 1-wire device I could find. Unfortunately I was not able to get them in the SOT-223-3 package which is the smallest package I might be able to solder. Instead I went for the TO-92-3 package which is through hole and easy to solder.
On the upper side of the hanging hole you can see the copper wire I used to make sure that the PCB and the hook are in contact. I did the same for the hole for the ring, but only on the lower half. The ground wire of the DS2401 is connected to the ring hole and the 1-wire data pin (pointing up in the photo above) is connected to the hanging hole.