See my reply #5 on the new ECU part number. In reply to your coded key query, the K4 - L1 Wee does not have a transponder to ECU built into the key. It does however have a security feature built into the ignition circuit, to limit theft through hot wiring.
There is a post on
https://www.DL650.org/pbsoluces-entretien.html, the 3 rd item from the top with the title "Bégé - infos sur le débridage de la DL650 K4 K5 et K6" which is for the earlier K4 - K6 Wee (title translation english "Bégé - info on unlocking the DL650 K4 K5 and K6").
Not sure if this mod will work on the K7 Wee, as the ECU on the K7 was changed from a 16 bit ECU to a 32 bit ECU. But if your ride has only one spark plug per cylinder and the idle screw on the frame on the left hand side, then you may still have a K6 but first registered was in 2007. If you do try the mod, you do it at your own risk.
The 4th post has info on the K7 on model
https://www.DL650.org/photos/pbsoluces/zop/debridage-k7/index.html. Once again info used at your own risk.