Yeah… I think a metalic map will be your best bet. (try maybe a solid grey? so its 50%~ish)
But You could also try messing with the reflectance of the mesh and if your skybox is a certain color it should reflect the skybox depending on the situation.
ORRRR you could code something that determines the light levels around the hair and changes its metalness or reflectiveness respectively.
or maybe mess around with custom normals? idk