A surface coating in Mechanical automatically creates shell elements on the element face that share nodes with existing elements. I have used it for coating with isotropic materials. I don’t know if you can assign a material direction the way you can with surface bodies.  Try it and see.

The table you show for a Lacore panel represents the rigidity (EI) of the panel made from a sandwich of a specific honeycomb core density and thickness and a specific facesheet material and thickness.  That is different from the properties of the facesheet alone. To use that data in Ansys, you would separate the E from I and then break I down to a thickness because those are the inputs needed in Ansys, there is no input for EI.  Then you would use just a surface to represent the sandwich panel and assign that material along with the thickness of the panel. That will create a model that will have the correct stiffness, but you won’t know the stress in the individual layers in the sandwich. You won’t know the shear stress in the core or the tensile stress in the facesheet.