"I am looking for an approach on how to provide the input control for the uifigure"
Idea 1: add buttons to your App
One approach would be to simply add 4 buttons to your App.
Each button could use the same callback function that changes x (or whatever other variables they should affect) depending on which button was pressed.
Idea 2: use uiconfirm()
app.UIFigure = uifigure();
selection = uiconfirm(app.UIFigure,'Select something','MyApp',...