In the current work, we investigate the transformation mechanics of gold-silver nanoparticles with cuboctahedral and icosahedral geometries by varying relevant attributes including size, composition, morphology, and chemical order. Our findings reveal that the transformation occurs via a martensitic, symmetric mechanism, irrespective of the specific attributes for all nanoparticles under consideration. The associated transformation barriers are observed to be strongly dependent on both size and composition as the activation energies increase with higher silver content. The chemical order is also a significant factor for determining how readily the transformation occurs since core-shell nanoparticles with gold exteriors display higher barriers in comparison to their silver counterparts. Likewise, for a given composition, core-shell morphologies indicate reduced ease of transformation relative to alloy nanoparticles.