Silver bismuth sulfide (AgBiS₂) nanocrystals have emerged as a promising eco-friendly, low-cost solar cell absorber material. Their direct synthesis often relies on the hot-injection method, requiring the application of high temperatures and vacuum for prolonged times. Here, we demonstrate an alternative synthetic approach via a cation exchange reaction. In the first-step, bis(stearoyl)sulfide is used as an air-stable sulfur precursor for the synthesis of small, monodisperse Ag₂S nanocrystals at room-temperature. In a second step, bismuth cations are incorporated into the nanocrystal lattice to form ternary AgBiS₂ nanocrystals, without altering their size and shape. When implemented into photovoltaic devices, AgBiS₂ nanocrystals obtained by cation exchange reach power conversion efficiencies of up to 7.35%, demonstrating the efficacy of the new synthetic approach for the formation of high-quality, ternary semiconducting nanocrystals.