Zinc oxide provides strong protection against UVA and UVB radiation. Does $\ce{ZnO}$ retain this protection when it is dissolved in oil?
When $\ce{NaCl}$ is dissolved in water, the $\ce{Na+}$ and $\ce{Cl-}$ ions are pulled apart by the water molecules. I would assume that a similar thing happens when $\ce{ZnO}$ is dissolved in oil, where the $\ce{Zn^2+}$ is separated from the $\ce{O^2-}$ ions.
Also, according to Wikipedia — Zinc oxide,
ZnO reacts slowly with fatty acids in oils to produce the corresponding carboxylates, such as oleate or stearate.
But that still doesn't tell me whether that would lead to a loss of the UV protective properties.