If the external HDD is in the Mac OS Extended (HFS+) format, you can use Time Machine without reformatting the external HDD.
Anyway, selecting the files and folders and dragging them onto the external HDD will work, though I don't know what Option/Alt + Command + Spacebar does to your files, as it open the SEARCH THIS MAC window on my Mac OS X 10.6.4 Mac.
Just open two different Finder Windows, one showing the external HDD, the other showing the internal HDD and drag the files and folders to the external HDD.
You can also take a look at CarbonCopyCloner or SuperDuper to clone folders onto the external HDD if you don't want to use Finder and its DRAG & DROP capability.
Btw, what exactly do you want to save? Your settings, mail, bookmarks, videos, ...? Are all your files in the
Home folder? If so, cloning your Home folder will suffice. You can use CarbonCopyCloner for that.