My dogs like to eat cat poop. So we keep the box in a closet with an idea similar to Brandons, however instead of a rope we installed a chain lock. It opens wide enough for the cats to get in but the pups don't fit. You could also try that with food.
My neighbor learned her cat to open a kitchen cupboard to get to his food bowl. She had Aussies and it foiled them, so I imagine a shiba would be stumped. Any cat worth it's salt should be able to open doors, as Sumo did.
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