A constant 5V buffer circuit
You will want to place a capacitor in the circuit that holds a charge from the battery voltage of the first battery through the switch over time. This capacitor will provide the temporary supply to the input of the voltage regulator circuit that converts the battery voltage to the controller required +5V.

This capacitor will need to be isolated from other loads on the quad so that only the 5V converter draws energy from the capacitor. This isolation can often be provided using an appropriately selected Schottky power diode. 

Selection of the capacitor value will need to be made based upon the available voltage levels of the first battery and the current draw of the controller as reflected back to the input of the 5V converter. That data has not been provided so no direct recommendation can be provided other than to suggest trying out what is needed on an experimental basis.