Well, if you're running 8.0 or 8.1 Data ONTAP, you can temporarily disable the ASUP message for USER_TRIGGERED to your .to and .noteto recipients.
Invoke your fake USER_TRIGGERED (WEEKLY_LOG). Then reinstate your .to and .noteto destinations.
For 8.0 instructions, see KB: 1913810
https://kb.netapp.com/support/index?page=content&id=1013810
In 8.1, use the "autosupport trigger modify" command for the "invoke.all" event.