With the upper PCB removed, you can now flip it upside down and desolder the Omron Switch. (Make a note of which way the switch is facing!)

Clean off any excess solder from the component mounting point of the Omron switch.

Mount new switch on with the white click button facing the same direction as the old switch.

It's okay to burn the switch a little (since it's dead anyways right?) but try not to let the soldering iron touch any of the other solder points when soldering/desoldering the new/old switch.