It is a problem with children.
I made bedside cabinets (about 750 tall and 500 square) and put a lock on the one on my side when I realised the children were of an age where they were liable to go "exploring" - that's children for you
However I am fairly sure the elder (but perhaps not the younger) did find the handcuffs and similar and, without doubt, correctly put 2 & 2 together as he aged... oh well... by the time they are grown they should be able to accept that parents are people too.
I don't like the cupboard/picture idea. It's too narrow, you'll need a lot of shelves in it, someone will bang their head on the door and "stuff" will be too easily knocked from the narrow shelves onto the tied person below - perhaps causing injury. I would not want a pair of handcuffs falling on to my face/head from 1m above!
If you are a firearms owner you could install another "gun safe" in a bedroom wardrobe and tell the children it's for ammunition storage (as required in Oz) - they won't get into that!
Otherwise how about putting swivel castors on your existing box in order that it may be easily rolled to the other side of the bedroom out of the way of the play space?