What a dilemma!
What about thinking this way: if you ctb, (and I'm sorry for this), you won't care about your stuff and this world anymore because you will cease to exist. So, what if they read your diaries? Who cares?
Also, if you thrown them away it's the same.
I think your family will like to have some kind of memory of you and they could even know more about you in that way. (Even though you don't want them to read them)
Anyway, that's my opinion.
Hope you can find a solution to this issue and wish you the best.
I'm really gonna miss you.