Plastic zip-ties would hold them, but I'm not sure of how securely when loaded.

You'd have to cut them with diagonal pliers to remove them, which would be easy.

I have fiberglass boxes on my Giant rack, but I secured them by drilling seven holes in each and tie-wireing them on with 14 gauge galvanized wire.
I can't get them off now, and it looks like barbed wire.

Photo:

The left box is kind of lifted up by the pull of all those bungee cords.
The right box has a five pound lead acid battery and stays down.