I would connect to 4 pins, say 4:7 and then set the pin change interrupt which will trigger as soon as a button gets pressed (assumptions 1. you've debounced the switches and 2. they're on the same port, although not entirely necessary).
Your ISR can determine which switch has been pressed and pass this information on to a post-interrupt function where you can use your switch statement if you choose or have a separate function for each button. From a guideline perspective, I prefer the switch function when dealing with state changes rather than singular events in which case dedicated functions are preferable. Makes it a bit easier to understand for the guy that has to clean up afterwards.