Horn of any kind requires no finish if the material is sound.
Wood is dependent on type- I use a mixture of tung oil and linseed oil if I want to darken wood. It's my belief if you are not using wood like ironwood which is particularly dense you ought to consider sending what you intend to use off to a stabilizer- essentially an acrylic material and often dyes are drawn into the wood fibers replacing moisture and empty spaces... stabilizing it.
Otherwise, you can be happily shaping away on a scale or handle block and a big chunk of wood flies off...rendering your piece either unusable..or at least requiring major repair work to complete.
Woods like walnut, maple, and any wood with spalting in it needs to be stabilized.
I'm not an expert..so wait to hear from others who are further along the path than I am.