I've got this Fujitsu laptop with Bluetooth built in, and it gives me enough space to use this small Targus Bluetooth Mouse on the tray table onboard United Airlines.

I've done this a few times. It's probably not officially allowed. I really don't know.

The Targus Bluetooth Mouse has an on/off switch on the bottom of it, so I don't think I'd ever remove the batteries as a precaution to anything even if they told me I couldn't use it. There's very little chance of it accidentally being switched on.