The problem here is knowing where all the files are. Are you sure you could list all the places eg ms word stores cached copies of your document? And that you’d be able to overwrite the data from copies that have since been unlinked from the filesystem?
Encryption is a better solution, always. It’s easier to forget a passphrase and render the key useless, especially if you’re using a SSD where the controller has no obligation to actually overwrite a cell that you’re trying to shred.
My understanding is that shred hasn't been reliable for many years now due to smarter and less predictable firmware in modern storage devices. Basically, you can't trust that your SSD deleted the data it said it did, or that it writes data to the place you told it.
So far as I know, wiping free space is a feature that has been available for many years in free utility suites and even recovery software (CCleaner, etc). I believe it's also directly available in Windows' Disk Cleanup utility; on Linux you call just use dd to fill the disk. This isn't as secure as a multiple wipe, but it can also be done multiple times; on Linux you can alternately use tr or some such to tell dd to write ones instead of /dev/zero.
Wiping free space doesn’t wipe the original location of a remapped sector. AFAIK, nothing will short of low level format, which you can’t do these days.
I'm not sure if it's feature of all modern SSD or Samsung ones, but I know that those SSD use AES internally for all data (not for encryption specifically, but because they need random bits for better storage and encryption is just a bonus). User usually does not deal with it, as it's handled in firmware, but BIOS have the option to securely erase the disk which just generates new key instantly and then, obviously, it's not possible to recover any data from old sectors.
