lol don't do this
And exactly why not? The shotgun is disabled, the action cannot be worked, and a shell cannot be chambered. So, tell me what's wrong with this method, please.
In case I wasn't clear before: The OP has a pump action shotgun. Open the action, run a cable lock up through the magazine loading port and out the ejection port. Lock it. Keep the key. This can even be done with a loaded magazine tube.