I was concerned about coming out to my father as well, but knew I would have to if I wanted to start transitioning. By that point, I really did. The dysphoria was only get worse every time I slipped back into denial and about a year back, I decided I wasn't going to ignore it anymore. Basically my entire family knew I was attracted to females by this point; I originally just told my parents, but eventually it trickled to everyone else and all of my family seemed to pretty accepting about it. However, this did not ease my nerves about coming out as Trans. When there was a trans rights bill brought up on the News, my dad would always joke around (as he does with most things he should take seriously) and say that it doesn't make any sense that laws could pass that would allow all of his colleagues to dress like women at work. In short, I really didn't think he'd take me seriously. He also has somewhat of a temper and I feared for the worst alternative which would involve him lashing out at me. Eventually, I told him and he said, "I'm not surprised. What else do you have to tell me?"
At first, I was relieved, but then I realized he actually didn't understand at all. He started throwing out alternatives to my decision like "just being happy with myself" or "enjoying the comfort of a female body". I spent about a 3 hours explaining to him how it wasn't the same thing and that I wish he would understand. He initially told me that he would try, but that if I came out to him expecting that he would help me pay for hormones or surgeries that "it wasn't happening". He took me to a therapist to talk about my problems and I ended up talking about how I wanted to start hormones to her, but she actually wasn't very learned in trans-issues and would much rather talk about other things, so I stopped seeing her shortly after. Nearly six months went by before I did anything else. I slipped into denial again because I had an abusive girlfriend who failed to understand that GID wasn't an issue with how other people saw me - it was my mind telling that believed I was a male, but knew that I would not be seen that way by others or even myself because I could not even look into the mirror without being overcome with immense enmity for the body that I saw but never seemed like it was the one I was supposed to have. Because the girl didn't understand (or more like refused to), she called me selfish, superficial, and stupid - or at least that was her entire point of her ten minute diatribes.
Eventually, I was desperate to escape our relationship, despite this girl ruining my relationships with everyone else I knew. I pleaded to my father to understand me and help support me, because I really couldn't wait anymore. I sent him a seven or so page email about how I felt in harrowing detail. When I came home later that week, he told me he wanted to to talk...and he understood. He admitted to me he didn't know how to handle it the first time I told him because he had never been personally exposed to someone who was Trans before - but that what I told him was alarming and he only wanted to help me if I felt so poorly about myself. Four months later, I started HRT. He is now discussing with his company to see if they can offer an insurance package that will cover my surgeries. He corrects my mom when she forgets to call me by the correct gender pronouns. I guess what I'm saying is that a lot of people are afraid or hesitant about things they don't understand, but if your father really cares about your well-being, he will come around. Sometimes it just takes time for things to process things. I gave my father processing time unintentionally (because of ->-bleeped-<-ty people in my life) and got lucky that the third time I confronted him was when he finally understood that it wasn't something I could just brush off or get over. If you are really afraid of how he reacts, tell him how you feel slowly and just don't shove your entire emotional journey at him the first time you tell him. If the reaction is bad, then you have other people who support you, right? I had a really hard time, because only a few fickle friends of mine knew before I came out to my parents, but I'm assuming that's not the case for you. If he freaks out, you can always try again at a later date. But be persistent of it. Tell him that you aren't telling him to anger him, but because it's really important to you and you are hoping that he would try to understand.