It turned out that my old Internet-Box Plus (and not an IB2 like I mistakenly wrote) can also be used as a wifi access point, with some careful changes in the router configuration.
First of all, save yourself time and DO NOT DO A FACTORY RESET of the box, like I did.
Because if you do, the IB will need to be re-provisioned again by Swisscom, and you will need to connect it to the ADSL/VDSL line in order to download a configuration from our ISP. Wasted a lot of time doing this, but hey, it was a test!
You need to reconfigure the box from its web interface, available either at http://internetbox.home or the old IP address used by the box as a router. You might want to use an ethernet cable to avoid any issue with wifi, should you have the same wifi setting on both the new and old routers, like it was my case (of course!).
REMEMBER: use one of the yellow switched ports to connect to your LAN!
Since I reprovisioned the box from Swisscom, I also needed to create a new admin password, which is easily done from the login page at: