I am not on HRT yet, but I have been pondering on how this wil go for me.
I believe talking with him alone is best, and it is also best to be sure both of you will have plenty of free time for the conversation and for the afterwards.
I'd begin it with something like "Dad, you know I love you, but I have been suffering and went through something really hard. There is something very important you must know"
From that moment on, he knows you mean to say something important, and there is no turning back either. I'd describe things that happened with me during my childhood and teenage years, and early adulthood as well. Then I would get straight to the point and tell him I am changing genders.
I don't know if this would work for you, I don't even know if it would work for me! It is what I came up with though.