Simple order cancellation in Drupal Commerce, with 24 hour time limit?
I haven't tested any of this, but you might some of the following useful:

Entity Operations allows you to take a Rule and turn it into a menu tab. This would be one way of getting that onto the order view page.

Something I've really been wanting to try is the Entity action links sandbox:


  Allows actions and rules components to be executed via AJAX links on entity view.


Just note the patches discuss in the Sandbox README.

If you wanted to do the Rules route, these would be probably your best option, because you can use conditions and components to provide some sort of response or action system based on the order status and time.

Otherwise, you'd need to create a custom module with a custom access callback that does the appropriate checks and then executes the action if allowed. (For a developer, I think this would actually be an easier route.) But the rules stuff is intriguing.