What right of yours is being violated if you refuse?
Further, to require me to submit to the search before engaging in LEGAL activity, they are, in fact, violating my 5th Amendment rights against self-incrimination. They are forcing me to perhaps incriminate myself.
What crime are you planning on committing that you require prior protection from self-incrimination? By your logic, it is illegal for you to carry a gun onto a plane, so therefore to search you for that gun would violate your right not to self-incriminate yourself. In which case, you are free to violate the law at will, and there's very little point in even having such a law. Is that really where you want to go with this?