When I told my T I was self harming, I first explained why I did it and ended with "and that's when/why I hurt myself". That way you start with something 'easy' to tell and it doesn't come out of nowhere when you say it, the way it would if you'd say "By the way I've been thinking about death a lot lately".

I agree with the other people that replied that it's unlikely your therapist will be disappointed.