I’ve created a case mod for the Pibow that gives a Lego button cap for the joystick on a Display-o-Tron 3000.
The key element is slicing off the lower ring from a 1x1 round plate. This reveals an indentation which exactly fits the nub of the DoT3K’s joystick. From there you can mount any 1x1 round brick, and have it protrude through the top layer by drilling a simple hole.
The 2x2 flower (Lego part no. 98262) works brilliantly as a thumb-friendly joystick, like it was always meant for that purpose. Plus it has the Lego logo imprinted on the stud, which I find somehow more gratifying than the swallow-safe open studded pieces.