Stuff that's printed on old photographic paper cannot be recycled because of the chemicals used in the developing process. Same with anything done through photo processing (printed on heat-sensitive paper, etc.).
But digital prints—for instance, something you just send through a good-quality printer—are more akin to glossy magazine photos and can go right in your recycling bin.
TL;DR version: if you can easily tear your headshots, they're more likely the latter than the former.
