Having failed to actually find anybody advertising specifically nickel-free earbuds I looked for some inexpensive ones which were likely to be nickel-free. I chose the plastic Sony MDR-EX10’s. I picked the white ones figuring that they won’t have any metal in the paint given it’s not a metallic color.
I found a lot to like about these headphones – the sound quality is good and the provided soft cups fit my ears well, block out a lot of background noise and give good bass.
But are they nickel free? Turns out they are. Even the metal 2.5mm connector is – I scraped it in case there was some coating to wear away and expose nickel later. The plug tested negative (i.e. no nickel).
So there’s a recommendation for earbuds.
If you’re looking for full size headphones then Marshall’s specifically state that their headphones are made with nickel-free metals. These are much pricier than the Sony pair I bought; they sell earbuds and headphones.