Bypassing input capacitor with a microcontroller
If you can solve this problem using an analogue switch part. Use the switch to short across the capacitor when the switch is actively closed.

There are many analogue switch parts available in the market place. Selection will depend upon a number of factors: 


Number of switches you need in one package
Frequency response you can expect through the switch when it is ON
Analogue voltage range allowed through the switch with a given voltage/gnd rail supplied to the part. 
Series ON resistance of the switch on ohms. 


If you are not looking for the highest in performance the application that you showed may very well be met using a 74HC4066 or similar type part.