You don't need to enter the product key to upgrade to Windows 10 from 7 or 8.
Also a new key for Windows 10 will be generated and saved on the Windows license server under your machine key.
If you make some types of changes to the hardware in Windows 10, you make need to re-activate Windows 10. Usually it's a just call to an automated process attached to a license server.
If you do a clean install of Windows 10 overtop an already activated Windows 10 version, you can skip the product key entry and your version will be re-activated from the license server if the hardware ID is the same (or make that telephone call to the automated licensing system).
I just went through this process:
- Install Windows 7 Pro in VirtualBox.
- Upgrade that to Windows 10 Pro.
- Download the Windows 10 Pro ISO.
- Re-install, a clean install, of that ISO in Windows 10.
Except for the Windows 7 install, I did not need any product key.
So, in short, you don't really need to worry about this anymore.
There are many product key finders: Belarc, Magic Jelly Bean, Produkey, ShowKeyPlus, KeyFinder, productkey.vbs, etc.. All of these are free or have free versions.
Another useful thing (if you save detail), is the signed license manager data. In an elevated command prompt type:
slmgr.vbs /?
for command list
slmgr.vbs /dlv
for licensing details