Stop using the damaged control and arrange model-specific advice. An air button is part of the operating arrangement, and damage should not be dismissed simply because the surface button does not contain the motor wiring.
What the observation tells you
Do not seal a cracked bellows with tape, inject liquid into the button or disconnect tubing to test it. Note any water entry, intermittent operation or change in how the button feels without repeatedly pressing it.
A useful next step
Provide the disposer and accessory details. For applicable InSinkErator installations, check the manufacturer's current UK safety notice as part of that assessment rather than assuming every air button has the same risk or remedy.
Manuals and supporting guidance
Model-specific instructions take priority. These references support the practical principles discussed here; they do not diagnose your appliance.