The only tool i know of that could possibly do it would be BartPE if you loaded the drive in a external enclosure. But even then it is a long shot. From what i seen there is a add-on to the BartPE that will allow you to recover the serial from a different install.
Any other tools will only recover the serial from the install that is currently active. So it wouldnt get the serial of the install on your External but the install that you booted with.
Any other tools will only recover the serial from the install that is currently active. So it wouldnt get the serial of the install on your External but the install that you booted with.