Thanks to a tip from Bethany, I got hold of a bottle of Skin Biology's Calypso's Oil. It couldn't be simpler; there are just two ingredients. Ethylhexyl palmitate is a derivative of palm oil and it has a 'dry-slip' feel that is similar to some types of silicone. The other ingredient is squalane. This is usually derived from olives or wheat germ (although less scrupulous sources include shark liver oil) and it penetrates well and isn't greasy. Squalane is especially good for those with very dry or traumatized skin or acne.
I've been using Calypso's Oil - the basic, non-perfumed one - to nourish my finger nails with very good results.