The Covert Razor Blade. It's non-metallic. Wear-resistant. And razor sharp. Indefinitely, they say. The non-dulling blade is made from zirconia ceramic, a compound significantly harder and tougher than metal. In addition to the main straight edge, the Covert model also has a chisel-ground corner edge so you'll always have 2 cutting surfaces to choose from. A lanyard hole is included too in case you want to sew it into your clothing (do not recommend underwear) or cord it to your belt or gear.
According to vendor ASR Tactical, the Covert Razor Blade was originally designed during the Cold War for use as a low-profile, non-metallic operations tool. And by "operations tool" I mean hide-out blade for cutting tape, ropes, plastic cuffs, and KGB faces. Some Amazon reviewers complain about its small size (30 mm x 10 mm), but I think the whole extreme sharpness and longevity in a thumbnail-sized package thing is the entire point of the razor. I just wish it had a handle and soap strip on it.