It is definitely okay to do it in an email.
There are also other ways to do it:
- Talking with them (the one you don't want)
- Writing an email
- Writing a letter
- Writing a letter and giving them to read, while you are there
Whatever you choose is okay. There are definitely other ways I'm not thinking about right now.
I was pretty sure my parents would be accepting and it was still difficult to say. I'm certain that is even more difficult if you don't necessarily expect them to react well.
Good luck