Several "real" file systems have mount options to wipe file when deallocated. It really slows down must system so you don't see it used very often. Other filesystems will write zeros on allocate.
One thing you can do complete defrag your disk. That will consolidate all he free space. Then write a file of all zeros using all he free space. hat should get things cleaned. However as someone else side, if he OS has bits and parts in things lichee Registry, then you need to find something to clean that up.
Confidential or not, some places run a drive wipe program before disks are taken out of service. They write a radon pattern over the whole disk, then all ones, then all zeros, then a different pattern. In all about 7 passes. It takes a bit to run. If that is not done, then drive gets put in a degaussing machine. In many cases after either of these, the drive is then crushed.