For a panel in pure bending (i.e. Mx or My), I don't think panel buckling comes into play. You can have local instability.
For example, for a honeycomb panel in bending, the top facesheet goes into compression and the bottom in tension (or vice versa), then the top facesheet can have wrinkling, dimpling and/or crimping, all local instability modes. However the panel would not tend to buckling in this situation.
For a stiffened panel in bending, the face would be in compression and the stiffener in tension and again, you could have local buckling of the skin or cross-section crippling (both of which HyperSizer accounts for), but no panel buckling mode.
For panel buckling, HyperSizer uses only the Nx, Ny or Nxy loads.
Please let me know if this answers your question.
Phil