I would worry about some paints with the bath oil, but worth a try. ( A tangent for Avon, 'Lectric Shave, Old Spice and other colognes are decent small area paint/ink removers. The plastic finish was fine on the few I've tried. I'm not to sure the smell is better... 
)
When I painted for a living, baby oil and bath oil removed paint from face, hair, and other areas of the body a solvent wasn't at all welcome on.
It creeps under some and lifts, so wash off well. (a lot of oils can do that)
