Employing 6 hats thinking isn't based on an awareness of "which type of hat I am," because such thinking goes entirely against the 6 hats system. The first part of the idea of 6 hats is to use (or "wear") each of the 6 hats one at a time. The second part is to wear each hat in parallel with someone else's hat selection.
This doesn't entail thinking the same thoughts as someone else, but only to wear the same hat. For example, if both of us have chosen to wear red hats at the moment, then we will both put forth our own emotional red hat thoughts, such as, "I hate this idea," "I love this idea," "I'm bored with this idea already," "I have a bad feeling about this," "The Mariners won last night!," etc.
White hat thinking is informational. "George Washington was born in the state of Virgina."
Yellow hat thinking is optimistic. It always finds reasons why something is valuable, why it must work, etc.
Black hat thinking is cautious. It always finds reason why something won't or might not work. Black hat thinking warns about the possible consequences of taking an action.
Green hat thinking is creative. It finds alternatives and makes suggestions based on lateral thinking and the like.
Blue hat thinking is organizational. The 6 hats system is a product of blue hat thinking processes. Blue hat is focused on planning a course of action.