I personally would use Acronis to do this by making an image of my current drive, then restoring the image to the new drive. Acronis is paid software so it isn't for everyone (but it is by far the best way to create proper images of drives that can be browsed)
The Samsung software should be work just fine for your use though. Just add the nvme drive to your system, boot up to your HDD, run the program which will do its thing then turn off, disconnect hdd and boot to nvme drive.