I haven't read the entire post, but I wanted to give my input. In my opinion 10% isn't enough to claim unless you idenify enthnically or you have been disadvantaged by it in some way. Otherwise its an injustice to minorities, namely blacks and hispanics.
Will you get caught in a lie? Doubt it, so go for it if you can live with it.
Its an interesing subject though, I am half mexican but have green eyes and am very light. My mom can sometimes pass for white even though she is 100% Mexican. Some people say you can't tell there is any Mexican in me at all, but then again people stop and speak Spanish to me all the time. Then there is my niece who is 25% black with blue eyes and light brown hair. She is as light as me, the only give away is her hair texture and curl. I am definatley Mexican because I was raised by my mother and maternal family, just recently connecting with my father and his. Same goes for her, she is black not soley on the basis of 25% but also because she is in touch with it.
On the other hand, 100 or so years ago you probably couldn't vote, own property or go to a good school...so maybe somehow those disadvantages have trickled down to you and you need that extra boost on your application. I'm mostly kidding.