Is it permissible to carry one's maternal aunt on one's shoulders for fun, given assurance that there is no risk of temptation?

Your joking with your maternal aunt in the manner described - especially if she is of an age where she is desired - could lead to dangers and open a door to fitna (strife/temptation) in the future. Satan lures a person towards indecency, and Allah the Almighty has warned against following the footsteps of Satan. Islamic law came to block all means (to evil) and prevent what leads to falling into the forbidden. Therefore, caution is obligatory.