I don't see why you'd want to use a switch statement at all, for that problem. It seems to me that all you need is:
A constant array of integers holding the size of each die you're supporting.
A state variable which is an index into that array, identifying the currently-selected die.
Some event handling code to increment the selected die variable modulo the number of dice.
Some event handling code to generate a random number within the range of the currently-selected die and pass it to a display function.
A display function that renders a specified value on your display.
I'm not clear how you'd display any value over 9 on a seven-segment display, but presumably you have a scheme in mind.
ETA: Or in other words, I agree with Jimmy60. 