If you have the drive space, you can keep all your cd keys installed to sep profiles. Perhaps name the profiles Key 1, key 2 etc. When you want to change cd keys just copy the dii folder from the profile you want to the cd key you want to change. Make sure you delete all the files in the folder you want to change before hand.
To install to the sep profiles, you'd have to set privacy to the documents and settings folder. The only way to access the cd key for that installation shortcut would be to login to the profile. The only other option I can think of is to install dii, then rename the folder, install another copy of dii, rename that folder, so on in succession and then make diff shortcuts. I guess it just depends on how much effort you want to make.
However, without profiles, the diabloII registry entries has the install path in there. I'm unsure if running the shortcut with a diff location would run those files, or if the registry would run the files in the default path.