Yup, that works, but it can be done simpler.
Here's one way if you've already got a cap soldered to the board: Use a SPDT on/off/on. You wire cap 1 to the board this one's always on. Then you wire one lead of cap 2 to north pole of the switch; one lead of cap 3 to the south pole; and the other leads of both caps to one side of C1. Then you run a wire from the center (common) pole of your SPDT to the other side of the C1 input cap. In the center position, only the stock cap is active. Thrown one way, cap 2 will be connected across C1, adding its value to the capacitance. Thrown the other way, C3 adds its value.
But wait, there's an even easier way to do it. Use an on/on/on SPDT. Put the smallest value you want on one side of the switch, the middle value on the other side of the switch, and both of their other leads on one side of the cap's spot on the baord. Now wire the center pole to the other side of the cap's spot on the board. Thrown one way, C1 will be in the circuit. Thrown the other way, C2 will be in the circuit. What happens when you go in the middle? Both caps are on at the same time, adding their capacitance together, creating a third cap.