I didn't really say anything to my distant relatives. Just updated my name and made my gender visible on Facebook. A few of them messaged me to get clarification. Like Elis said, if you don't see these people a lot, this doesn't need to be very personal. Whenever I write, I like to use the "what-so what-now what" model to get things across and that is probably the simplest way I've found to get everyone on the same page.
What - I'm writing because I wanted to let you know that I'm transgender.
So What - I'm still the same person I've always been, but I may start to look and sound a little different as I continue my medical transition.
Now What - I'm going by Max, and I'd appreciate it if you used male pronouns when referring to me (he/him/his). Feel free to reply if you have any further questions or if I can clarify anything for you.