Buy a cheap, wired usb keyboard and mouse.
Once you have an OS installed, start using the wireless keyboard and mouse.
Oh and one more thing: the NUC you bought comes with USB3 ports only. This means you won't be able to install Windows 7 unless you add the USB3 drivers to your install media.
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I have been checking this thread and I was wondering, if you were able to resolve this with the information provided above.