i’d have used the pen.
if that wouldn’t have worked i’d have cut an airway in his trachea and put a straw or pen tube in there temporarily.
Even if you performed the procedure correctly and gained access to the trachea, a cricothyrotomy probably wouldn't have helped in this case, because much of the critical airway constriction is further down in the smaller airways of the lungs.
However, it might be helpful if the kid was also choking on a piece of the cookie.