I'm going to agree with Synthfreek on this one. If you change the iTunes music folder in advanced preferences to the new external drive then consolidate iTunes will copy everything over to the new drive AND use the files on that drive. If you simply copy as I suggested it will continue to play the files off of the original drive and once you reformat it you will need to delete the old iTunes library and add all of the files back into the new iTunes library. Easy enough to do but consolidating is easier.
This will not work
Changing this setting does not point iTunes to existing files. It only determines where iTunes will place any files added after that point. When you add a file to the library iTunes records the path to that file and looks for it in that location from then on. If you move the files and then change the iTunes folder to match the new location iTunes will still look where the files were, not where they are. Consolidating instead of copying changes the pointer and takes care of that problem,
This will not work
However, it should be pointed out that the drive letter assigned to a given external drive may be different depending on what computer it is connected to. In which case the iTunes program on each computer can easily be pointed to the iTunes folder on that drive by going to Edit/Preferences/Advanced within the iTunes program.
Changing this setting does not point iTunes to existing files. It only determines where iTunes will place any files added after that point. When you add a file to the library iTunes records the path to that file and looks for it in that location from then on. If you move the files and then change the iTunes folder to match the new location iTunes will still look where the files were, not where they are. Consolidating instead of copying changes the pointer and takes care of that problem,