Switch/Pushbutton for Multiple LED String Lights
A single pole dual throw ( SPDT )  switch or button should be sufficient for this.

How you wire it will depend on exactly what that "battery-pack" does. It may me possible to wire it directly to the LED strings as shown here..





However, if the drivers are more complex current drivers, it may not be possible to switch them safely down-stream of the regulator. Something like the following circuit may be required to switch a separated battery to each regulator.







simulate this circuit &ndash; Schematic created using CircuitLab