I don't know how often you see your parents, but I believe coming out is best done face-to-face if possible. (My parents have been dead more than 15 years, so you can disregard my advice.)
I wouldn't worry about causing them great emotional harm if you come out to them honestly, earnestly, and with love. I came out to my family in baby steps, sort of. My sister was born in '36, my brother in '40. They know what transgendered means and what transsexual means. They are of an age (chronologically and era they were raised in) to not want to talk about the medical or sexual aspects.
I first explained that I am transgendered - that I had been wearing women's clothes since I was about 9. After that sank in for a while (week, month, whatever) I told them I was starting to live full time as a woman and was changing my name to Katherine. I didn't mention hormones or whisker-clearing until they could begin to see the results. I have not broached the subject of surgery.
When talking to your parents, you want to talk about feelings and how you fit into society and how long you've been troubled by this. You do
not want to talk about sexuality or how you hate your penis.
Just my 2ยข.

Good luck, Pippa.

- Kate