Zeroizing external hard drives

So we had two laptops that bit the dust on us (screen problems). I removed the hard drives and planted them in cases to convert them to external hard drives. Right now I'm re-formatting them but want to zero them out. I checked out DBaN's website (http://www.dban.org/) and I've heard they're a good source to use. But everything I'm reading says to download the program to a disk then boot the computer from the disk to zero out a hard drive. I'm worried doing it that way will screw up my current laptop. Does anyone have knowledge on the best way to zero these out without messing up my current laptop? Or at least know a better/different program to use?

 
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