I think if there was just one object that most audiences would associate with Claudius, it would have to be poison. Consider the many different associations and connections he has with it. First, he poisons Hamlet's father by pouring poison in his ear. Then, he plans to poison Hamlet during the fencing match at the end of the play, both with a poisoned cup and backed up with the poisoned tip of Laertes' sword.
Of course, metaphorically, Claudius is a poison in the kingdom. Like the poison itself, he is a silent murderer and a hidden threat to everyone. He brings deception, corruption and a dangerous desire for power to Denmark.