This works fine for me when it comes to finding out what my product keys are. I use both 32-bit and 64-bit. I just save a screenshot of the produkey window.
ProduKey - Recover lost product key (CD-Key) of Windows/MS-Office/SQL Server
I doubt you'll find the Windows 10 product key externally. Windows 10 is kind of different from previous Windows when it comes to activation and reinstallation. I think it's better now.