Can I use Index Dat Spy to delete index.dat files?

Yes. Using Index Dat Spy, open the index.dat file you're interested in. Then, from the File menu select Delete on Windows Restart. The current file will be marked for deletion when you next restart Windows. 

Note that many index.dat files are required by different parts of Windows and although it is safe to delete them an empty replacement will be created during Windows startup. Therefore even though you mark a file for deletion on Windows restart, you will probably still see it after Windows has restarted. However, if you open it up in Index Dat Spy you should see that the file contains a number of blank records and little else.