Classic IS the carbon installer in this instance

Someone from Blizzard mentioned once that since the installer works in Classic and Apple still ships Macs that work with Classic, then they have no real need to spend resources on a Carbon installer for a 3 year old game.
The installer should work fine in Classic. If you don't want to update your OS 9 System Folder to get Classic working, then that's your choice. The only other way would be to install it with someone else's computer and then copy it over onto yours. I believe the CD Keys are embedded into a couple of the data files during installation so they should hold over in a copy.