We elucidate the effect of lattice mismatch and chemical ordering on structural transitions in bimetallic nanoalloys of ∼1.5 nm. We show that collective screw dislocation motions happen in small mismatch shell@core systems while strongly mismatched ones favour incomplete outer shell rearrangements. Cooperative transitions can also become hindered when the chemical ordering breaks the geometrical symmetry. Escaping from an unfavourable morphological basin occurs first via re-arrangements of the geometry and then changes towards a better chemical pattern. We observe that the chemical re-ordering mechanisms are independent of system composition and stoichiometry but hinge on the initial and final chemical arrangements.