No, I wouldn't but this is a 1 for N scenario while stealing information is N for 1 - hackers hardly target a single persona and if they do, they won't get stuck on your intimacy rather than any information that can make their trouble worhwhile. Aka, person of interest, aka, non regular user. I'm sorry, but I find your point a bit extremist.
The reason I wouldn't be willing to deliver this information (my IMing history) is not because I have something to hide, but things I don't want to scream for the world 'hey, come look at my IM history'. It also contains things I would be judged on and would have to explain for randoms - things that do not need to become public and this poses a difference - you can get most of this information by asking.
I don't want people to see how I talk to my wife, or my customers, my boss. But on the unlikely event that this history is leaked, I wouldn't be harmed in anyway, aside from the fact that some would find me stupid, others cute, others smart, others wouldn't care.
I understand your right to privacy, but I still do not get the extreme concern about IMing softwares. You have a personal email, do you think your information is safe there?