I thought instructions to have two installs of Complete Chronicles were on the wiki at some point, but I can't find them anymore. So this might be useful:
Since you already have DI installed, you can simply rename its installation folder (for instance, C:/Program Files/Uru/Deep Island instead of C:/Program Files/Uru/Complete Chronicles).
Then, put the CD in your computer again, and choose "Uninstall". Since it won't find the game files, it won't delete your DI installation.
Then, the "Install" option should be available again. Make sure you reinstall it in another location than DI.
A shortcut to the offline install should be put on your desktop, you'll have to make another to Deep Island's UruSetup.exe.
If you already uninstalled all the game files:
First install the offline version (for instance, in C:/Program Files/Uru/Complete Chronicles). You should have a shortcut automatically installed on your desktop
Then copy ALL content from the installation directory to a new directory (for instance, C:/Program Files/Uru/Deep Island)
Use the DI patcher on the Deep Island directory, NOT the Complete Chronicles one. Create a shortcut to the DI UruSetup.exe.