Don't listen to the people who tell you that you should always do the same thing in the same situation. It's OK to mix up your play (and necessary against people you against on a regular basis). That being said, bet this flop at least 95% of the time. I don't really like your reasoning for checking behind here because it makes it sound like checking behind is actually the better long-term play, which it isn't. The only reason you should ever be doing it is to confuse your opponents and not let them know that if you don't c-bet a draw-heavy board, it means you missed the flop.

Also, I doubt that this nit is a tough enough player for mixing it up to be worthwhile against him.