I understand that you have erased Windows 10, preinstalled on the e-MMC card. In order to install Windows 10 on your NUC, no additional drivers are required on your installation USB. You need to prepare your installation media correctly (my advise is to use Microsoft Media Creation tool):Download Windows 10 . Doing so, you will have the latest version of Windows downloaded to your USB media. Your USB will be bootable too.
Install Windows according to the following tutorial: Windows 10 Forums . Skip on para 12 and install Windows with UEFI bios as described in para. 13. In step 13.B, take care to choose the right partition for Windows installation.
Once your installation is completed, install Intel drivers downloaded here: Downloads for Intel® NUC Kit NUC6CAYS . Instead of downloading each driver separately you can download Driver Bundle zip and unzip it on your drive. Install all driver manually (do not use Intel Driver Update Utility). Start from installing Chipset driver and reboot your NUC. Install all the other drivers. You can reboot your computers once only, after all drivers are installed.
Hope this helps.