From my perspective, trying to send messages that always fail and waiting for exception is just a waste of resources. Therefore I would consider having a parameter at customer level (not necessarily in CustTable) and checking it already in CustInvoiceJour.sendElectronically(). If it's not active, I wouldn't bother trying to send the invoice to customer.
If you look closely, you'll find that such logic is already in place for a few countries (based on CustTable.eInvoice checkbox).
Nevertheless if you want to change the log only, start looking at from where SysExceptionLog gets called.