The electrochemical cell offers the promise of enabling controlled alteration of the morphology and islanding phenomena on metallic surfaces. Different diffusion processes near step and island edges are known to profoundly affect the growth mode, island sizes, island shapes and step morphology. Using the surface-embedded-atom model (SEAM) modified for the electrolytic environment, we calculate the dependence of the activation energies for these diffusion processes on the electrochemical potential for the Ag(100) and Ag(111) surfaces. While all these processes show some degree of dependence on the potential, the step-edge barrier and the edge diffusion processes are the most sensitive. Step-edge barriers for Ag(111) increase (to over 1 eV) with a 1.0 V potential (relative to the potential of zero charge (PZC)). The variations for Ag( 100) are not as large (about 0.3 eV), but the excess step-edge barrier can be negative for high positive (> +0.6 V) or negative (< -0.4 V) potentials owing to the competing roles of hopping and exchange diffusion processes and their dependencies on the potential. Edge diffusion decreases rapidly with potential for both (100) and (111) surfaces. Significant variations are also found for diffusion around corners and kinks, which play important roles in island morphology. We assess the influence these variations have on island sizes, shapes, diffusion, and coarsening. From this discussion, we show how the electrochemical potential can he used to control the fractal or compact nature of islands, and the magnitude and scaling exponent for island diffusion and coarsening.