By playing it "cool", do you mean cold? No returned affection?
Well, this is my opinion, if you could handle the pressure.....I think it would be to your advantage to act as if you were not interested in her affections toward you. If there is one thing that makes a woman want to get a man's attention....it's when he's not interested.
So, how are your nevers? Like steel? I'm wondering just how cool you could play it. The big challenge is not playing it as in "cold" but by being "nice" but not interested. "Thanks mam, but just not interested in what you're offering" kind of attitude. Like a cowboy who tips his hat and gets on his horse and rides into the sunset with the lady looking longingly after him.... wondering why she couldn't interest him. Wondering why he prefers to be with his horse more than her.....(lol).
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!