You can perform multiple experiments to illustrate the contributions to the hyperfine fields. In these experiments the center of the carousel will represent the position of the nucleus, the electrically charged ball will represent an electron and the bar magnet can be used to represent the spin of the electron.
To illustrate the orbital contribution put a kid with a magnetometer at the center of the carousel. Then place the electrically charged ball somewhere on the carousel and make the carousel rotate. The circular motion of the electrically charged ball will create a current loop, which will generate a magnetic field. The kid can measure the magnetic field with the magnetometer.
To illustrate the spin dipolar contribution we do a similar experiment, except now we place the bar magnet somewhere on the carousel.
I think the Fermi contact term cannot be illustrated with the materials at our disposal.