You have to connect Via ethernet - then you can connect Via the wired IP and change the Wifi information...

On the Wall clock you can get to the RJ45 connector easilly at the underside of the unit itself (right side)... Just needs an RJ45 - RJ45 cable to hard wire - connect the other end to your Router ideally.
On the desktop it's a little more difficult as you need to take the front off - the sides will become loose, and by removing those you should be able to get access to the connector on the Pi.
In a perfect world if you know you are moving/changing providers, Set up the new wifi before the old one is disconnected/unaccessible. I completely get that it's not always possible though.