Check with the maker. SOME compasses use alcohol, others use mineral oil, still others use "compass fluid" which is similar to but not the same as mineral oil. Using the wrong fluid can change the damping AND dissolve the printing on the card, or cause the seals to leak again.
I think Ritchie used to have a special exchange program, swapping your compass for a rebuilt one at 1/2 of list price. It's worth asking them.
And if they'll sell you "compass fluid" that's meant for your compass...that's what I'd use, just to be safe.
Baby oil smells good because it has fragrance added to it. If you use mineral oil--use the plain pharmacy grade kind. Fragrance just can't do any good inside the compass.