Your transition is about you, not about pleasing others. Whether people are happy for you or unhappy/angry with you is something you have no control over. You will have some people in each category no matter what you do.
I understand the reluctance to alienate your family members. We all want them to accept us. I was lucky that my parents had both passed on before I thought about transitioning, so I didn't have to face that particular fear. I did have a brother that I was worried about. When I came out to him, he surprised me by being totally supportive and accepting. Sometimes we worry for nothing.
I won't lie to you: in some families it doesn't work out. Parents do sometimes reject their kids, and when it happens, it hurts everyone. But you have to ask yourself if it is worth giving up the chance to be yourself in order to keep your father happy? And, as you say, it may end up hurting him more anyway if you don't come out.
