Yes, you can change to a wireless setup.

You should be able to update the Wi-Fi credentials for the Amp using the app when you have that network up and running, however, to get the Play:3s to use the router’s Wi-Fi, you will need to factory reset them. See Unsupported Products here https://support.sonos.com/en-gb/article/connect-sonos-to-a-new-router-or-wi-fi-network

Edit: if they Play:3s are being used as surrounds with the Amp, I would remove the surrounds prior to the move.

The play 3rs will be in different rooms and will have to be Wi-Fi too. Does that make sense ​@Mr. T 

Yes, that makes sense. You can just factory reset the Play:3s to join the new Wi-Fi network.

If you’ve ever entered your current Wi-Fi credentials into the Sonos app and intend to use the exact same SSID/password at the new location, then it would just be a case of amending the new router’s SSID/password and everything should just connect again when powered on.