My son was rather older than you look to be when he came out to me. By this time, he had been living independently for years, and he emailed me about being trans. Both he and I are pretty verbal people, printed or spoken, so that kind of communication is fine for/with us. Is it something for you and your parents? Maybe a voice recording would be better? maybe call the answering machine, ensuring that they're not going to pick up while you're talking?
I do think it worked well for my son and me that he was able to go through the things he wanted to say without me interrupting. Even to jump in with 'yes I love you' probably wouldn't have worked as well. So paper, email, or phone message might be better than face to face conversation. Since my reading between the lines included a lot of him saying 'Please don't hate me', my email reply went with several repetitions of 'I (still) love you!'. Since he'd started by email, I answered by email (within the hour of getting his note), but asked about phoning him. When he replied, he did ok phoning, so I did. And things proceeded well from there. You might consider suggesting that they respond by writing (or phone message that you do _not_ listen to in real time)? A way to let you and them absorb the news and think about the real feelings, rather than immediately answering?
I certainly understand your concern, even with parents you're 95% confident will respond ok. It took my son years to come out, and it wasn't until it was basically a desperation move that got him over the hump of telling me. He'd known me longer, probably, than you've known your parents. And though I never mentioned trans*, I had mentioned/supported nondiscrimination against gays (which he also is). Still, he was scared to tell me. So you being scared too is no surprise.
But a word from the supportive parent's view (which is 95% where you think your parents are). My biggest sadness in his coming out to me was not that he was gay, or that he was trans, but that he had suffered so much for so long by _not_ telling me. I love my kid, and want him to be happy and healthy. Going through life as a woman was making him miserable and unhealthy. Happy, healthy gay+trans kid is enormously better in my parental view than unhappy, unhealthy pretending-to-be-straight+cis kid.
A different thought. Perhaps I and my circle are just about unique, or people like us just don't get much press. But I asked my son about telling other people, starting with immediate family, and even after my positive response, he was very concerned -- about his safety. So he said, a big point, that he trusted me to tell only people that it would be safe to tell. So far, that's everybody in the family, and all our friends. Maybe part of it is how I present it -- poppa bear does not take kindly to people who are mean to his kids. You might mention something about whether/who your parents should/shouldn't tell about you being trans.
From the parent's side again: Answering a few of their likely questions is a good idea, but I'd suggest limiting that to the top few. And then go to the "These are things you can do to help" suggestions. I asked my son this, as he'd focused initially just on how he knew he was trans+gay and how much living otherwise was hurting him. For him, top desires were for me to use his male name, and the male pronouns. Whatever yours are, let your parents know. If they're coming from my view (I want my kid happy and healthy, what can I do to help this happen), they'll be very concerned about this. Having a couple guidepoints, if not a full roadmap, will be helpful.
Good luck!