Yes, you can disable the WiFi. Wired devices will still get internet connection when the WiFi is disabled.
To disable the Wifi from the app, click on the Settings gear in the bottom right corner. Under WiFi, click on Advanced. At the bottom of the Advanced page, click on Wireless Settings. At the bottom of that page, you will see a button where you can toggle the WiFi on or off.
To disable from the Starry Station, click on the settings gear. Click WiFi and enter your PIN. Scroll down to the bottom of the screen. Under Advanced Settings, click on WiFi Radios. You can toggle the WiFi on or off by clicking the button next to WiFi Signals.