Switching between two power supplies to power bluetooth board
Are you powering the BT board directly with a 24V supply? Most BT boards/modules cannot handle more than 5V unless there is a regulator on board which converts higher supplies to the appropriate supply voltage. Even then 24V is high. Connecting a 24V supply might fry the board.

That switch would work (though it might be overkill considering its ratings). Something like this would be more suitable and inexpensive. You'll need to tie all the -ve wires together. The BT supply wire (or +ve) will go to the middle pin of the switch, the wall wart +ve and the battery +ve can go on either of the two ends of the switch pins.