It is not unusual for a small nonprofit to hire an independent contractor as its executive director and authorize that person to sign documents and take other binding action on behalf of the corporation as the CEO.  It is not dependent on whether the bylaws specifically recognize the existence of the ED position; the board has authority to delegate such responsibility as it wishes.  If you want this person to have such authority, you ought to be sure that it is specifically approved and in the board minutes.  If you don’t want the person to have such power, you will probably want to change the title of the position because a person called the executive director would probably have “apparent authority” to be able to bind the organization in relations with third parties.

In either case, you want to be sure that the person is actually an independent contractor and not an employee.  The IRS is generally skeptical about the classification and assumes that the organization has the power to control the time, place, and manner of execution of the duties of an executive director.  If you lose that debate on an IRS audit, you could be liable for a lot of back taxes that you failed to withhold because you misclassified the person as an independent contractor rather than an employee.