Separate PSU or integrated into the device? (I don't know much about the Shield).

If it's a separate PSU: The last time I had a PSU that made a high pitched whining noise, I contacted the manufacturer and they sent me a new one which didn't have the whining problem. No questions asked, they just sent it to me. I didn't even have to send back the old one. I was dealing with a different device and a different company, so I don't know how yours will handle it, but it's worth a try.

I also seem to recall getting similar excellent service, regarding PSU whining noises, from another company in Cambridge several years ago.