The influence of electronic shell effects on the barriers and channels pertaining to metal-cluster fission is studied using a shell correction method in connection with an asymmetric two-center-oscillator model potential. This approach has the advantage that the ensuing shape parametrization allows for an independent variation of the deformations of parent and daughter clusters. Results for both symmetric and asymmetric channels associated with the parent clusters Na-10(2+) and Na-18(2+) are presented. We find that barriers, which separate the parent configuration from molecular-type configurations associated with preformation of the fragments, are most important and must be considered, together with the subsequent separation process, for proper elucidation of metal-cluster fission phenomena.