We put the child with the magnetometer in the centre of the carrousel.
We put the bar magnet (to simulate electron with spin) at the edge of the carrousel. This bar magnet has a magnetic field. We measure it’s magnetic field at the centre of the carrousel (the position of nucleus). The field that we measure there is the spin dipole contribution to the magnetic hyperfine field. (Note we did not regard possible rotation of the carrousel.)
Now we regard the turning of the carrousel (so movement of electron) and only look at the charge of the electron (so we remove the bar magnet and place a negatively charged ball there to simulate electron charge). The charge moves so we have a ring current, which generates a magnetic field. If we measure this magnetic field at the centre (position nucleus) we would find the orbital contribution to the magnetic hyperfine field.
Our magnetometer cannot be penetrated by our bar magnet or our charged ball in the carrousel analogy. Therefore I think it is not possible, in this analogy, to measure some kind of Fermi contact contribution, which would be due to magnetic fields generated by electrons inside the nucleus.