Recovering Files From Old Hard Drive Question

So I recently transferred all my data to a new, bigger hard drive. Went perfect except for one thing. I didn't realize that in order to recover my girlfriend's saves I needed to log into the ps4 with her user and do that also.

It's not a huge deal, but I'd like to recover her Diablo 3 character from her user and transfer her save over to my new ps4 hard drive.

If i put my old hard drive back in, will it just try right away to format it? Or can I refuse it (like by staying offline or something) and still get her file onto a usb?

Basically, to sum, is it possible to recover a save from an old hard drive that's not currently in use?

Thanks!