According to the EFF, any third-party headphone maker will not have an easy task making headphones for the Shuffle however as they will need to use an "Apple authentication chip" for the headphones to even work with the device.
Headphone makers could, normally, reverse engineer the interface but the chip makes it illegal to do so and any company found doing it will have the DMCA thrown at them.
A review at iLounge summarizes the DRM:
"This is, in short, a nightmare scenario for long-time iPod fans: are we entering a world in which Apple controls and taxes literally every piece of the iPod purchase from headphones to chargers, jacking up their prices, forcing customers to re-purchase things they already own, while making only marginal improvements in their functionality? It’s a shame, and one that consumers should feel empowered to fight."