One option is to modify the mechanical latching mechanism so that the “radio button” functionality is removed.
In reality, I think you’ll find that you could remove the latching mechanism and replace it with push buttons mounted onto a plate, maybe made of plastic or aluminium.
Yes, that’s possible in several ways. Either by holding a ‘previous button state’ value for each switch, then polling each button in turn with a timer to test its current state and compare it with its previous state.
The other way is to use interrupts, either RISING, FALLING OR CHANGE.
Either solution will need a debounce routine, as no mechanical button/switch ever makes/breaks the contacts cleanly.
Given the fact that you need to monitor 4 buttons, interrupts are the best solution.
Pete.