I just told my Mom two days ago. Going to tell my Dad next week, though I'm sure that he's already heard it from my Mom. She took it way better than I expected she would. I was really nervous about saying anything to either of them, sort of taking your approach of "deal with it when it comes up".
Not knowing anything about you, it's hard for me to give advice. I'm older, have my own health insurance, and I'm going to see a therapist. The last time I was talking to my Mom, we were complaining about health insurance, and how so many things aren't covered. I casually dropped in that the therapist I'm going to see isn't covered by my insurance (because GID isn't covered). It was an easy way to segue into the topic. She asked what I'm seeing a therapist for, and I tell her that I'm going to see a gender therapist. I know she was shocked, but she took it really well. I told her that I'd been feeling this way for years, and that I finally decided to talk to someone about it.
For myself, bringing it up earlier was better. This way, no one is shocked about any drastic changes. We'll see how it goes with my Dad next week.