As I understand it, there are two possible approaches:
An analog input can read actual voltage, and make decisions based on the reading.
A Comparator circuit can switch a digital input when the voltage falls below a pre-set level.
finding a spare GPIO pin (digital) is easy enough, analog inputs are a lot less available.
Want to make it universal? design it to interface by USB.
What should you worry about? Your new device causing battery drain.
Since you are designing electronics any way you go.. How about a re-chargeable battery replacement? Might require some isolation tricks since the board is not expecting charge voltage, but it would be less complicated than monitoring for failure.
One other related note: There is a variant of the "standard cell", a bit harder to find, that holds the voltsge at peak much longer, then eventually falls steeper. But this is a good fit for our issues.. I THINK it's a "BR" instead of "CR" battery number.. no notes in front of me right now.