I feel your pain.

I would very much recommend the following -

Back up the drive to an external drive. In this, you'll have access to all the info on that drive or possibly boot up on another Mac if need be. Goal is to keep all your data to date.

Next, go thru the usual pains of reformatting the internal drive. Go to the disk utility and do an "erase." Do the full erase not the free space. Ideally this should be done at least 3x if you really want to make it difficult to recover wiped out files. Only those with appropriate tools that want to recover some data would be able to do so. - I wouldn't worry at this point.

Final step is to install a fresh copy of the operating system and any other softwares you sold along with the laptop.

Trying to delete out sections as you suggested leaves room for error and someone with an "undelete" software might be able to find what you deleted. - Even if you use the wipe free space from the disk utilities.

There are other ways to achieve the above but I think this is easiest. It does take time but its worth the peace of mind and also having a "copy" of the entire disk bootable on another Mac (incase there is data you need).

- Phrehdd