Although a mezuzah is very holy and must be treated with the greatest respect at all times, the fasting custom you mentioned only applies to Torah scrolls and tefillin. The son who dropped the mezuzah is not required to fast even if the mezuzah fell without any covering at all.
It is true that it is customary for all who witness a Torah falling to take on a fast day, if they are able. But this specifically applies to Torah scrolls as it is a communal responsibility to guard them. In contrast, even if one witnessed tefillin dropping, he would have no need for any atonement.
Moreover, fasting inevitably weakens the body and would interfere with your boys’ Torah learning — the greatest merit of all! On that note, as a positive outcome of this experience, it would be a good idea for them to learn through the laws of mezuzah.
It is customary to contribute something to tzedakah to atone for the unintended disgrace of Hashem’s word.
 Agur B’ohalecha 4:27; Sha’arei HaMezuzah 18:5; Tzitz Eliezer 5:1:99. Cf. Maharsham 2:264.
 Piskei Teshuvos 402:13, citing Mishpetei Shmuel 12.
 Sha’arei HaMezuzah 18:5, citing Mishneh Halachos 5:195 and Shraga Hameir 3:12.