If you know Elite, it has space stations where you dock by going inside, while matching station's rotation. That's only in one axis (and note the hangar goes through the axis of rotation, i.e. centre of mass). To add rotation around another axis would make the task impossible.
Wikipedia talks of "chaotic rotation" of astronomical objects, but only over long timescales due to gravitational interactions and thermal effects. On short timescales, its axis shouldn't change much at all, unless you bump into it and apply an off-axis torque.
[0] https://en.wikipedia.org/wiki/Precession#Torque-free_or_torq...
https://rotations.berkeley.edu/a-tumbling-t-handle-in-space/
You can demonstrate it at home with your smartphone (or, more canonically, a tennis racket), and see for yourself that the tumbling happens much too quickly to be explained by whatever force the air is imparting.