You don't have a custom header uploaded, so you needn't concern yourself with that. The "fallback mode" cart display should happen automatically on mobile devices, so there's nothing special you need to do to set that up.
I have sent a request to Development to add a certain tag to the fallback cart that should help improve the initial display, rendering the cart zoomed-in at normal width, rather than zoomed-out on a wider cart as some mobile browsers currently do. Currently, buyers should already be able to double-tap their screen to zoom in, or use the "pinch" touchscreen gesture to zoom in/out, swipe to scroll around, etc.