Many people have asked for this solution, however the most common answer is to use advaced MAPI with the Outlook Object Model or automate the clicking of a button. A better solution exists if you are willing to edit your registry.
The security popup is only triggered when attempting to use simple MAPI. Microsoft used to provide the settings in the outlook .adm policy file but the one the currently provide for download has unfortunately had these settings removed.
Microsoft policy files serve only as a GUI for setting keys in the registry so we can edit it manually or use code.
The key is : HKEY_CURRENT_USER\Software\Policies\Microsoft\Office\12.0\Outlook\Security
Each value can be set to one of the following: 1 (Default, PromptUser), to 2 (AutoApprove), or to 0 (AutoDeny)
So to disable the security prompt for Simple MAPI Mail Send (DoCmd.SendObject and such) you need to set HKEY_CURRENT_USER\Software\Policies\Microsoft\Office\12.0\Outlook\Security, PromptSimpleMAPISend to 2.