Typically, once the Windows 10 Enterprise LTSC (aka Windows 10 IoT Enterprise) has the key installed, there is no need to swap it out.
You could create a sysprep unattended file with the new key in a sysprep unattanded file. Run sysprep with unattended file on Computer A, and copy the image to Computer B. When Computer B boots, it will have the new key.
If this is an image you want to ship, you will want to create the image from scratch and setup the distribution share and answer with all the device drivers, applications, and settings so that get installed during OS installation. Better image management over the lifecycle of the product.
Regards,
Sean Liming