To answer your question, the latter....shell the money for a cable to plug directly into the hard drive to pull everything off.
The best option is to go to Best Buy and purchase an External Drive case with USB-C to SSD/SATA Adapter. Amazon sells External Drive cases too.,
When you get the case, insert the old hard drive into it and then just plug it into the USB-C port on another computer. This is the easiest (and cheapest) route to take. I'm not a hardware expert but I was able to do this myself without any problem.
How to Install a Second Internal Hard Drive on Your Windows 10 Device