Having a phone with no call log

There are a lot of questions asking about unlimited call log. I have the exact opposite problem: I want no call log at all in the software. Even with a phone with "pocket detection" and a complicated swipe pattern, I still happen to randomly call a number who called me previously and that I do not want to call (clients who do not see my number when they call me : I do not want them to have *my* number). For instance because of inadvertent manipulation, drop of water on the screen making the touch detection put my finger where it isn't, etc... I do not care about privacy issues, I just do not want to have any way to reach a call log with phone numbers from the UI. Is there any way to achieve that with android ? Maybe with a third-party phone app ?