How to back-up a hard drive without power cable connected?
This answer offers to possibly solutions.
Solution #1
One solution would be to purchase a different cable. One end should have a USB Type C plug. The plug on the other end depends on the drive you purchased. Below is an image of plug and port types.

You can distinguish USB Type A from USB 3.0 by color. If the port or plug is blue, then you have USB 3.0. If the HDD's existing cable has a USB Type A plug, then the new cable needs to be rated for a transfer speed of at least 480 Mb/s. Otherwise, the HDD's existing cable has a USB 3.0 plug. In this case, the new cable needs to be rated for a transfer speed of at least 5 Gb/s.
Solution #2
Use an adaptor cable instead of an adaptor. In this case, I would recommend a cable which is USB Type C male on one end and USB 3.0 female on the other end. This cable would be placed between the existing HDD cable and the Mac. This type of cable would be compatible regardless of whether the existing cable has a USB Type A or USB 3.0 plug. An example of such a cable is the Tripp Lite USB 3.1 Gen 1 (5 Gbps) Adapter Cable, USB Type-C (USB-C) to USB Type-A M/F, 6-in. Length,