Jay
Generally, since the library is the publisher, they do the registration. You could always check with the library if you are not sure. I would NOT go ahead and register it without checking first since it might complicate things unnecessarily.
In Ireland and I assume the UK you may register the track but only the publisher can register their interest in it, you can’t. So in light of this I would let the publisher do it, it is in their interest to do quickly after all.