As with the compass, the orientation of your magnetic dipole against the field is unstable, so now you need a second propulsion system for maintaining the unstable orientation of the dipole.
Reaction wheels saturate and are therefore more suited for precise attitude control than as a source of sustained torque. Once they saturate you need to unload the accumulated momentum via some other mechanism. Thus, you do need a second propulsion system such as thrusters, light sail etc.
You can take the momentum back out of the wheels by rolling the magnet to the other side of the unstable equilibrium so that the wheels have to accelerate in the opposite direction to keep it steady.
[0] https://en.wikipedia.org/wiki/Reaction_wheel