Personally, I'd be less that thrilled at the idea of surpressing error output -- it might actually help the user to know that something is wrong.
I've had some luck (it depends a little on what you want to do) with changing the 'execute or die' syntax to an 'execute or assign the error to a subroutine'.
Your error subroutine could then distinguish between errors as a result of access levels vs. error as a result of the database itself... and act accordingly.