Formatting and wiping are two different things.
Wiping overwrites the data on the drive making it unrecoverable if done properly.
Formatting rewrites the file system but leaves the data untouched. A file recovery program could recover much of the data.
Depending on what you want then your suggestion of putting the hard drive in your laptop and reinstalling the operating system is practical.
However, replacement of a screen on a laptop is expensive you need to ask yourself who would want to buy the laptop.