For the CDT-TX-02M-R, can I interface to a microcontroller instead of mechanical switches?

As the CDT-TX-02M-R requires its switch inputs to be connected to ground to activate them, configure your microcontroller output pin as open collector/open drain to ground. This avoids any accidental current flow between the CDT and microcontroller if the voltage supply used for both are different.

It is also possible to use an external transistor/resistor to achieve the same effect. This would act as a buffer for the CDT-TX-02M-R and microcontroller.