Taka, I created a new thread for us for this one.
Let's get some other opinions.
For me, if I say "He wouldn't do that," I'm sure he wouldn't do it.
If I say "I think he wouldn't do that," I'm not completely sure he woudn't. It's not a very common construction. It's the sort of thing you say in the middle of a dialogue, to clarify or empahasize a point that may have been lost.
A: Peter and Mary. Now that would be a couple.
B: You think Peter will ask Mary out?
A: No, I think he will NOT do that, despite saying he would. He's still in love with Betsy. But time will tell, I guess.
If I say "I don't think he would do that," I don't see a lot of difference, but it's the more natural order. It doesn't have the same emphasis as the one before. (To me, it's also less certain than the one before, the "I think he will not" structure.)