Extend the metaphor and Claudius is clearly the mouse, the play designed to trap him, to catch him with the cheese as it were.
I like the image of Claudius as a mouse. It diminishes him in a funny way. It’s not the Bear Trap or the Lion trap. It makes Claudius a poisoning nuisance rather than a large threat.
I myself am afraid of mice – though I know that fear is unfounded. But even if you’re not afraid of a mouse, you still don’t want one in your house. Claudius as a mouse, hides in corners – scurries from one bad deed to the net – looking for things to chew up and consume. Claudius – The Mouse King.
The Hamlet Project 