Is expiation (kaffarah) obligatory for the oath "By Allah, if you return to your mischief, I will show you" if the boys did return to their mischief but were not hit?

If someone takes an oath to do something, and then sees that something else is better, he must expiate his oath. And refraining from hitting children is more appropriate. The expiation for an oath is to feed ten needy people, or to clothe them, or to free a slave. If he cannot find any of these, then he must fast for three days. If you carried out your threat against them, your oath is fulfilled and there is no expiation upon you. However, disciplining children is the responsibility of their guardians, and it is not permissible for you to fulfill your oath if you do not have permission to discipline them. Rather, you must break your oath and offer expiation.