I don't think there are any shortcuts, though it would be very handy.
The only way to really do a clean Windows 10 install when you also need to upgrade your Windows 7 license is:
- Install Windows 7 with the key you have and make sure it is activated.
- Do an in-place upgrade to Windows 10, ensuring that Windows is activated afterwards.
- You're now free to do a fresh install of Windows 10. I believe they do something to tie the activation to the hardware, so I'm not sure about moving the license to another computer any more. This means Windows 10 is auto activates on the hardware without supplying a key, or at least that has been my experience so far.
Note that once your license has been upgraded, it's no longer valid for a Windows 7 install. This may have changed or been clarified, but was the case last time I looked at it.
Edit:
Here's two FAQs that various Microsoft threads lead me to on the topic:
The relevant q's and a's are:
Q: Can I use Windows 10 media to upgrade to Windows 10 and still take advantage of the free upgrade offer?
A: Yes. You will be able to download Windows 10 installation media to
upgrade qualified Windows 7, Windows 8 or Windows 8.1 devices to
Windows 10 and still take advantage of the free upgrade offer. Your
device will automatically activate online after upgrading to Windows
10 while the free upgrade offer is valid.
Q: Can I clean install (i.e. boot from media and install) Windows 10 on my Windows 7 or Windows 8.x device and still take advantage of the
free upgrade offer?
A: No. Clean installs of Windows 10 on a Windows 7 or Windows 8.x
device via booting from media are not considered “upgrades”, so the
free upgrade offer will not apply. For your Windows 10 installation
to be considered an upgrade, you must start installation of Windows 10
while booted in Windows 7 or Windows 8.x
If you attempt to clean install Windows 10 on a device that hasn’t
taken advantage of the free upgrade offer and successfully activated
Windows 10 online before, you will be prompted to enter a Windows 10
product key to continue installing Windows 10.
Q: After doing a free upgrade to Windows 10, how do I clean install Windows 10 subsequently?
A: Once your device upgrades to Windows 10 using the free upgrade
offer and activates online automatically, you will be able to clean
install (i.e. boot from media and install Windows 10) the same edition
of Windows 10 that you upgraded to on the same device during and after
the free upgrade offer.
...
The automatic online activation will occur seamlessly after clean
installing Windows 10 if the device had previously upgraded and
activated online the same Edition of Windows 10. No product keys are
required.
