A small "Faraday cage" may work. A Brass or copper screen box that would cover the encloser of your headphone amp. Thinking about it for a moment, I have seen various "metal" mesh containers and other "mesh" office supplies at Office Depot and even Wal-Mart. They are painted, so I don't know the metalurgy. I am certain that the stores would think not highly of anyone scraping the paint off of them before purchase, but they seem cheap enough. For a few bucks it might be worth a try.
Tubby
Tubby