We have calculated the activation energies for several single atom and vacancy diffusion processes on Cu nanowires with the axial orientation of < 100 >, using the nudged elastic band technique based on the interaction potential obtained from the embedded atom method. It is shown that the dimer-initiated local strain and its relief at the transition state have a significant effect on the characteristics of self-surface diffusion mechanisms on nanowires. Contrary to the case for cylindrical multishell-type Cu nanowires, the vacancy formation energy for rectangular nanowires is maximum in the core region and is nearly zero at the corner of the nanowire. In addition, the activation energy barriers for the vacancy diffusion processes taking place in the core region are found to be higher than those occurring near the corner of the nanowire. Our calculations further show that the vacancy diffusion processes taking place near the corner of the wire are dictated by the lower coordination of the surrounding atoms. From the structural investigation of nanowires, we have also established that multilayer relaxations for rectangular nanowires with smaller cross-sectional area cannot be defined.