Cabinet Latch like a Door Knob
Why not use a surface-mounted cabinet twist latch:
image courtesy of houseofantiquehardware.com
Or, if your pup likes to open latches by biting, use a recessed slam latch:
image courtesy of actronmfginc.com
also called paddle-handle push-to-close latch, to protect her or his teeth?
Of course, if the bin is large enough to trap a person, you do need an inside handle!