Yes, babassu oil (INCI Orbygnia oleifera (babassu) seed oil) is an oil, even though it is solid at room temperature. It has a melting point very close to our body temperature - 76˚F or 24˚C - which means it will melt upon contact with your skin. It is a non-greasy oil, meaning it feels a bit dry on your skin.
Its fatty acid profile is interesting. With 42% lauric acid (C12), 17% myristic acid (C14), 10% palmitic acid (C16), 4% stearic acid (C18), 15% oleic acid (C18:1), and about 3% linoleic acid (C18:2), it covers the range of fatty acids with a little bit of everything. Stearic acid is a great moisturizing fatty acid. Oleic acid is a great moisturizing and possible anti-inflammatory. And linoleic acid can help restore skin's barrier functions and reduce trans-epidermal water loss. Because of this higher level of unsaturated fatty acids, babassu has a shelf life of about one year - but I don't think anyone could leave it on the shelf that long!
Babassu is considered a great replacement for coconut oil. Coconut oil is generally considered a greasy oil, so if you substitute it, you will find your creation is more astringent. Here are a few ideas on formulating with babassu oil (substitute it for the coconut oil in the recipe). But be warned - this stuff feels amazing, and you might find yourself taking out a mortgage to get more!
I've heard it can be great in a lip balm recipe (I have to try that this weekend!)
Or what about a solid perfume? If it melts on contact, that would be amazing!