Ouch!
The data for iCal is stored at:
USERS / username / LIBRARY / APPLICATION SUPPORT / SOURCE
"SOURCE" is a folder. In it, there is one data file for each calendar.
Address book data is stored at:
User > Library > Application Support > AddressBook
However, I don't suggest you try working with the low level files. Why not boot from the CCC backup you made? You could then open iCal and export to a file on a usb drive. You could do the same with address. Then you could import them on the MBA after you reboot to your normal drive.
Another option is to run migration assistant and pick the old time machine backup to restore. You can later delete "extra" stuff brought over by migration assistant above and beyond calendar and address book stuff.
If the problem is disk space, I suggest you resort to an external USB drive. This would give you room to do a lot of things like restore the CCC backup to a bootable partition, boot from it and do the export OR do the migration from the TM backup to a bootable partition on the external drive, boot from it and do the export.
If you do decide to attempt a "shortcut" and simply replace the files in the folders I mentioned above, please make sure you back up the stuff you replace so you don't wind up without the ability to use address book or calendar at all. I had a TM restore with a minor glitch and mail.app failed to open after the restore. The quickest way to recover was for me to delete 15 gig of files in my library/application support/mail folder and start over setting up my email accounts from scratch. This was no big deal for me because my only copy of my email was never sitting in mail.app. After a rather long IMAP sync, everything was as it was before the Time Machine restore.
Hope you get everything back!
