The "small vibration" is Libration, and it does not imply that lunar axis changes orientation. It is caused by Moon's movement not being a perfectly circular orbit parallel to Earth's Equator with aligned axis.
Here's a description of the causes of libration from the Royal Observatory (check the linked page for graphics of each source):
Synchronous rotation and libration
The 27.3 days it takes the Moon to complete one orbit around the Earth is about the same as the time taken for it to complete one rotation. This synchronous rotation means that it always shows the same face to the Earth.
However, libration means that it is possible to see around 59% of the surface. It has three components:
i) Diurnal libration
As the Earth rotates the view of the Moon changes. An observer on the surface of the Earth sees slightly around the eastern limb of the Moon at moonrise. At moonset the same observer sees slightly more around the western limb of the Moon.
This arises from the changed position of the observer because of the rotation of the Earth. A parallax effect means that the Moon looks slightly different at moonrise and moonset.
ii) Longitudinal libration
The Moon moves in an elliptical orbit around the Earth. As a result it does not move at a constant speed (this is Kepler's second law)
However the Moon rotates at a constant speed. When it is moving faster in its orbit, this allows observers on Earth to see around the trailing edge of the Moon. When it is moving slowly it is possible to see around the Moon's leading edge.
iii) Libration in latitude
The Moon's axis is tilted by 6.7° to the plane of its orbit around the Earth. This means that sometimes the Moon's North Pole is tilted towards the Earth and sometimes tilted away.
As a result it is sometimes possible to see beyond the lunar North Pole and the South Pole is hidden. Conversely it is sometimes possible to see beyond the South Pole and the North Pole is hidden.
The combination of the three kinds of libration allows observers on Earth to see 59% of the lunar surface. However 41% remained hidden from view until the space age.
So in order to get Moon's poles position you just need to know where the Moon's center is, which is quite standard, and the position of the poles referenced to that center, which is always the same (not in RA/Dec but in true space).
There is a secondary effect of "wobbling" called Nutation, which is caused by the Moon on the Earth, not a movement on Moon itself.