Hamlet's Dilemma

I feel as if Hamlet should have killed Claudius when he had the chance.  To me I feel like he is wasting more time by just waiting for Claudius to make a sin.  Claudius had done the worst sinful thing anyone could have done which is murdering someone, let alone his own brother.  When Claudius was admitting his sins, Hamlet should have been more angry because Claudius was saying that he is still sorry but he is still keeping the crown, the wife, everything.  That shows me that Claudius does not really care because I know if I ever heard the truth of my fathers death I would not stop to get my revenge, I would never hold back.  I feel as if Hamlet killed Claudius when he had the chance no one woud have known that Hamlet killed him.