I fear that an HD wipe will wipe ALL the free space
Huh? I don't understand what you are saying.
First, on a hard drive, that is exactly what a wipe program is supposed to do. So nothing to fear - that is what you want.
Second, on a SSD, no it won't wipe all the free space and that IS the fear! That is, the fear is some personal, sensitive data might be left behind. This is due to the various load leveling features with essentially all modern SSDs - and this is exactly why a "wipe" program should NOT be used on a SSD.
Sadly, folks seem to focus on the wear (limited number of writes) factor of SSDs but that is a
misguided focus.
For what purpose do we wipe a hard drive? To ensure no previously saved personal data is left behind. In other words, for
security (or privacy) reasons.
Since wear leveling prevents a wipe program from touching every storage location on a SSD, a wipe program does NOT ensure security. And that is why wipe programs should not be used on SSDs.
And on SSDs it is NOT about putting a 1 or 0 in the storage location. Remember how HDs and SSDs store data. On a HD, a magnetic charge from the R/W head "physically" orientates the magnetic particles on the platters in patterns that represent a 1 or a 0. To illustrate, a particle arranged in a North/South orientation may represent a "1" while a particle in an East/West orientation may represent a "0". There is no actual numeral "1" or numeral "0" saved to the disk.
On SSDs, a "cell" is either charged (to represent a "high" or a "1"), or not charged ("low" or "0"). And again, there is no actual numeral "1" or numeral "0" saved to the disk. And yes, over time, this charge can fade away which is exactly why the data on a SSD periodically refreshes - well, as long as the SSD does not sit unpowered, sitting a shelf for several years.
So a "Secure Erase" program does indeed, hit "ALL" the free space - including the reserved over-provisioning areas, ensuring each cell/storage location no longer holds a charge.