I have a Roku 2, model 4210X. I turned off wifi by going to Settings, System, Advanced System Settings, Device Connect, then selecting Disable Device Connect. That works fine on mine. Does it not work on yours?
It does work on mine. It works great, and then a couple of months later the WiFi is back on again.
Ok, I checked mine, and sure enough, the disable box was checked, but the wifi analizer on my phone showed it broadcasting. So I went back and checked the enable box, then checked the disable box, and that turned it off. I wonder if a power outage could cause this. Well clearly the firmware is screwed up because the selection should be sticky, but lotsa luck getting Roku to fix it.
Well, I will follow this and see what solution you come up with.
Edit: One other approach to this is to send commands to the Roku to turn the radio off. This could be the sequence of remote buttons needed from the Home screen to enable, then disable, the radio, then go back to Home. That could be an Arduino IR transmitter. I've already built one of those, so if you go that way, I can help with the IR codes, etc.
But the other way is to send commands to the Roku via your router. If it's already connected via ethernet, then it already has a network IP address, so you can send it commands. I've never done this, but it seems you could have a scheduled task that sends the commands once a day. If you have a Roku app on your phone, I believe it communicates with the Roku that way.