I recently clean installed win 10 on my laptop, no hassles.
I used Microsoft's media creation tool (is this what your link goes to?) to make the installation media (USB flash drive).
If your computer came with win 10 or had previously had it installed and correctly activated, then my understanding is that it will automatically activate upon installation. No key required, it just works. Just make sure that you create a disk with the same version as you previously had installed (home or pro).