PK Finder is a portable tool which detects and displays your Windows product key. The developer says Windows 8-10 are supported.
Simply run the program and it immediately displays your Windows version and edition ("Windows 10 Home"), along with the product key.
Tap a button and the key is copied to the clipboard. Alternatively, clicking File > Save saves it in a text file.
The developer has also included assorted interface settings, including a choice of "Style" (Metro, Office, Transparent, VS2010 and more), colours and "border thickness". Seems like overkill considering most people will barely use the program once a year, but the feature is there if you need it.