Let me tell you a very classical way of looking at what you said. What I mean by this is that this is what you are kind of supposed to say as an answer to a question like this so take it as that kind of response.
The reason why you become shy around alpha males whereas without them you are "the cool guy" is because you know that you are not a cool guy and when you are around one you can see it because you have something to compare yourself to. I know this because I'm similar to you. Girls see me as the alpha male while inside I'm a loser. But the fact remains. To remove the feeling you have means to become yourself. That is the answer. The reason why you become introverted around alpha males is because if you continue trying to act cool around them everyone will see through it, not through the things that you say (because they obviously won't change) but purely from the body language. Also under stress it has been proven that the human mind is inefficient so in fact what you say will be affected by that stress that the alpha male is causing you. Funny how practically everything in life leads back to the one elusive and mind boggling state of being yourself

. (I have not yet reached it myself so I can't comment on its existence)