I am the OP: my advice to anyone with the same issue would be just get an old motherboard and do it.
I have a few hard drives, laptop and desktop IDE, which I would like to Secure Erase. I'm aware that other methods exist for removing the data, but this is the safest and most efficient, and it's the one I want to use.
I found someone else with the same problem here, and a reply said
It depends on the chips in the adapters (see hdparm docs). Mine don't
support it, and the only one of them that I can warn you about is the
Seagate desktop expansion drive, the others have no branding.
In man hdparm it says
hdparm provides a command line interface to various kernel interfaces supported by the Linux SATA/PATA/SAS "libata" subsystem and the older IDE driver subsystem. Many newer (2008 and later) USB drive enclosures now also support "SAT" (SCSI-ATA Command Translation) and therefore may also work with hdparm.
However, I bought one which is support to support SAT, and reflected on the word 'may'.
I checked out https://www.smartmontools.org/wiki/Supported_USB-Devices. This is a list of devices which support SCSI-ATA Command Translation. I got a Gembird AUSI01.
It... didn't work. Just said 'erase prepare: invalid argument.'
I checked the adapter via USBdeview. It's genunine: correct chipset and device ID. It was able to work with smartmontools commands that I tried. It just wouldn't do Secure Erase, despite reporting that the drive could do Secure Erase.
So, I give up. Unless you have an opportunity to test this before you buy it, don't. Just grab an old computer... these days people will give them away for free.