Toggle Switch to swap the connections of two buttons
If the two existing buttons do not share a common GND connection then you will need a four pole double pole (4PDT) toggle switch. Such switch has twelve terminals. 

If the two existing buttons share a common GND then you can get by with a double pole double throw (DPDT) switch. That switch will have six terminals. 

Here is how you would connect the button flipper switch when a common GND is in place.



If the two switches do not share a common GND then you would use the 4PDT switch and basically duplicate the above circuit on the switch for the other sides of each button.