If you fear for the confidentiality of data, you should have used encryption, preferably full-disk encryption (TrueCrypt has good repute). With encryption, you do not have to worry about the disk itself, only the key; destroying the key is as good as destroying the data. This makes the problem more manageable.
Assuming that you did not use encryption, and that you have a disk where a lot of very sensitive data has been written, and you want to destroy it beyond any recovery. Then you should destroy the disk itself. Don't shred the files, shred the hardware. You could employ other methods (melt the disk in a furnace, dissolve it in acid, wipe it with an EMP from a nuclear blast...) but the mechanical shredded is probably the safest to use in a home or small business ("safest" but not "safe": beware of trapping your hands in it !).
If the price of a new new disk makes you cringe and grit your teeth, then maybe the data is not really worth a lot ? Otherwise, there is no possible hesitation.