A person who is cunning is usually seen as an intellectual person that uses this to get what they want through forms of betrayal, deceit, or evasion. The reason for the use of the term keys is that the people, in this case maybe rich merchants or generals, are essential for the child/family member that wants to over throw the king. If for example these people are against the prince then he wouldn't be able to retain the power of the king after he is slain. Or the plan to over throw the king would just fail. So I see the sentence in laymen's terms as the traitor prince will try to get rid of the king once he knows no one important will go against him.