This seems a bit odd to me. Why would the WiFi device use the same address as the router? You would think that a device would get assigned an IP address via DHCP. Does the device not allow DHCP and how does it decide on what IP address to use? This seems like a bad design on the devices side.
Like most routers are configured to be DHCP servers as well so when devices connect to a network they will typically send out a DHCP Discovery message. It seems like you should be able to go and enable this function or hardcode a static IP address to this particular device.
I typically setup my home networks with a limited DHCP range so I can use the higher addresses for things I would like to have a Static IP. Webserver, Printer, Desktop.
Seems rather pointless to me to have the change your router setup for one device. But I don't know anything about that device but if just randomly selects an IP address when joining a WiFi instead of using DHCP or being able to hardcode it yourself seems like a failure on the devices end.