No, you don't want to alienate him or make him angry, and that's understandable. But neither do you want him to go into eternity without hope and without Christ -- and God may want to use you in these days to confront him with this sobering reality.
Pray, therefore, that God will open the door for you to talk frankly with your father about his spiritual condition. Sometimes the hardest people to talk to about spiritual things are those who are the nearest to us -- our relatives or closest friends. But remember: You are not alone. If God opens the door to talk with him, He will be with you by His Holy Spirit -- and He'll also be working in your father's heart.
During these days, let him know that you love him and you care what's happening to him. And let him know that because you love him, you care not only for his physical health but also for his spiritual well-being. Let him know, too, that you hope to be with him in heaven some day -- and you will, if he opens his heart to Christ.
Most of all, let him know that God loves him. He may not love God -- but God loves Him, and the proof is Jesus Christ. When we know Christ, nothing "in all creation, will be able to separate us from the love of God that is in Christ Jesus our Lord" (Romans 8:39).