You should be able to to find the avast Outlook/Exchange provider by double clicking on the avast (blue ball) icon in the system tray.
If you enable this provider, and Outlook 2003 is your only mail client then you do not need to have the avast Internet Mail provider active on your system.
The other alternative about which you asked:
avast Internet Mail provider > Customize button > SMTP tab > uncheck "Scan outbound mail" box > OK > OK