@franco65 

Simply, if you want to make the EAP using the Public IP address from your internet service provider, you can disable the DHCP function on the Edgerouter-4, which is similar working in the "Bridge Mode".

But the problem is, public can only supply only one signal device with internet access, the EAP225-wall is just an access point and it has no DHCP function. 

For example, if you connect the PC to the modem directly, the PC will get a public address and have internet. If you connect the switch back to the modem, and connect two PCs on the switch, then only one PC can get the public IP address to join the internet.

And that is the reason why the network need a router, to working as DHCP and NAT. With the DHCP and NAT, all the clients in LAN will be assigned IP address.

If you want the EAp225-wall use the public IP address, I am afraid that the clients connect to EAP cannot work properly.