Hello Michael,
I would suggest global option in application settings called "Hide on copy".
In case user copies username or password either by hotkey or double-click MacPass shall hide to tray.
Actually this is what users I believe doing always - hiding or switching application after copy done, so such option will save a lot of time for those who are performing a lot of such operations per day.
Similar option is implemented in Auto-Type (auto-hide before typing), but in some cases it is only required to copy one of the attributes.

Regards,
Nikolay