ashdisp.exe is the application for the icon tray but, I'm not sure it is a good idea turning off the access to the interface.
"C:\Program Files\Alwil Software\Avast4\ashQuick.exe" is exactly the path you must use into WinZip. Ah!, without parameters.
Do not mess
logs with
reports. The first ones could be setted to the minimum (Emergency). The reports could be disabled at Settings > Report (page). Both options I do not recommend indeed.
More information about the avast4.ini file you can see
here. There is not a posibility (that I know) to hide the icon anyway...
Wellcome to forums.