For what you want, I believe it would be easier to just manually select and copy them to where you want on the new drive to back them up. This way you can make all the edit you like to them there as well. If you used a backup program to back them up, they would most likely be compressed and you would not be able to edit them.
If you like, another good option would be to move all of your images into a folder on the new drive. Next, include
that new folder in your Pictures
library. This way you can access the images from the Pictures library with them still actually being saved in the folder on the new drive.
Hope this helps,