Can cosmic rays alone produce noticeable aurorae in bodies far away from the Sun?
You may be interested to learn that Jupiter experiences aurora on its poles nearly (if not totally) non-stop. These aurora never cease, because they do not rely entirely on the sun as their source of charged particles, instead receiving particles from the volcanic ejections of its moon Io, as well as from cosmic rays. Granted, these aurora are occurring in the ultra-violet, but they are still 'noticeable'. 

In short, yes aurora can be caused by non-solar sources, and conceivably cosmic rays at that. As to your other question concerning 'how much' of the aurora is due to which sources... I couldn't tell you how much of the auroras visibility comes from the sun, and I doubt there is much (or any) information on that subject, since determining the source of such convoluted light is likely outside the realms of both interest and empiricism. Perhaps you could pioneer that research? In any case, an intriguing subject to be sure.