To set up a wireless-only connection on Edge MC, make sure you have first set up your hardware.
First, log into the Configuration page on your Edge MC's access point.
From here, you can collapse the Wired connection tab, or scroll down to the Wireless Connection tab.
Ensure that the WiFi is set to enabled, then select your network from the dropdown. Upon selection, you will be prompted to fill out the network's password. It will look something like this.
At the bottom of the page, press Save.
Once saved, the circle next to the Wireless dropdown should become green after recognizing the network.
Now your Edge MC can run entirely over WiFi, and will not require a wired connection.