My immediate reaction to your question was to say "a snake" as the perfect symbol for Claudius. No matter how hard I thought about your question, I just couldn't change my mind (which I ended up finding quite funny).
Just as a snake poisons its victims through the venom emanating from its sharp fangs, Claudius poisons Hamlet's father even before the play begins and then injects that same "something rotten" into the state of Denmark. (This is not even to mention the poison on the end of the fencing sword or the poisoned pearl, . . . both of which lead to the aura of death at the end of Shakespeare's play.)
I found another good comparison in eNotes own character analysis of Claudius that also fits a snakelike description:
Claudius is shrewd and able, though not always ethical or moral.
Same with a snake, of course. Shrewd and able, snakes often swallow their paralyzed victims whole. Snakes ethical and moral? No, of course, as members of the animal kingdom, snakes act solely on instinct and are incapable of ethics or morality. Is this so different than Claudius, acting on his basest instinct of lust in order to insure the murder of Hamlet's father and the marriage of Gertrude?
I haven't even mentioned yet that the snake, as an animal, is usually used to represent evil in many cultures. Claudius is most certainly evil, and yet with a charm that was able to somehow beguile the queen. (So strange! I have always felt that a different Hamlet, written from Gertrude's point of view, would certainly be fascinating.)
Yes, I think an evil snake would be the perfect symbol for Claudius, considering he is guilty of nearly all of the seven deadly sins: envy (of Hamlet's dad), lust (of Hamlet's mom), greed (for power in the form of the crown), wrath (at Hamlet for ruining his plan), sloth (for procuring Polonius, Ophelia, Rozencrantz and Guildenstern to do his dirty work in spying), and I'm sure gluttony and pride are in there somewhere, too.
King Claudius is the monarch in the play "Hamlet" by William Shakespeare. He poisoned Hamlet's father, the King, in order to gain his throne and his wife. Hamlet spends his time acting like a mad man in an attempt to prepare his own revenge and vengeance for his father's murder.
Claudius is aware that his own life is in danger as long as Hamlet is alive and knows he must plot against him. Claudius is the bad guy in the play. He is also representative of Cain and Able from the Bible. Cain slew his own brother and Abel's blood called from the grave. In Claudius case it was Hamlet's father ghost that called.
If I were to choose a symbol to represent the King, I would chose to use an upside down crown with a dagger with a drop of blood coming off of it. I know he did not stab the king but in many ways he did stab him in the back because he had betrayed him.