Connecting SSD drive to another computer (different SATA cable) to uncorrupt registry files

I have an OptiPlex 7060 Small Form Factor BTX (purchased from Dell in June 2018), service tag .  I got a sudden blue-screen-of-death situation, which constantly tells me "windows\system32\config\system is missing or contains errors, error code 0xc000014c".  Tried all the recovery things suggested.

The final thing to try, apparently before re-installing windows and kissing my current setup goodbye, is to connect the SSD to another (Windows10) computer, and copy that (working) computer's windows\system32\confic\regback files to this SSD, and see if that works.  (Described here: https://www.thewindowsclub.com/0xc000014c-bcd-error

But I'm having a hard time finding a system that has the type of SATA cable that this drive needs, it looks different than most of them.  I've put a picture below of the drive and existing cables.  

Anyone know what kind of cable or converter I need?  I'm also under the impression that the SSD can just be connected to another computer via USB, so a connecter there would work well (I just need to access some files on the drive, not boot from it).

https://imgur.com/XvD0Xcm