The earlier study of $^{124}\mathrm{Ce}^{*}$ formed in the $^{32}\mathrm{S}+^{92}\mathrm{Mo}$ reaction at an above barrier beam energy of 150 MeV, using the pocket formula of Blocki et al. for the nuclear proximity potential in the dynamical cluster-decay model (DCM), is extended to the use of other nuclear interaction potentials derived from the Skyrme energy density functional (SEDF) based on the semiclassical extended Thomas Fermi (ETF) approach under the frozen density approximation. The Skyrme forces used are the old SII, SIII, SIV, SKa, SkM, and SLy4 and new GSkI and KDE0(v1), given for both normal and isospin-rich nuclei. It is found that the $\ensuremath{\alpha}$-nucleus structure, over the non-$\ensuremath{\alpha}$ nucleus structure, is preferred for only two Skyrme forces, the SIII and KDE0(v1). An extended intermediate mass fragments (IMFs) window, along with the new decay region of heavy mass fragments (HMFs) and the near-symmetric and symmetric fission fragments which, on adding the complementary heavy fragments, corresponds to $(A/2)\phantom{\rule{4pt}{0ex}}\ifmmode\pm\else\textpm\fi{}12$ mass region of the fusion-fission (ff) process, are predicted by considering cross sections of orders observed in the experiment under study. For the predicted (total) fusion cross section, the survival probability ${P}_{\mathrm{surv}}$ of the compound nucleus (CN) against fission is shown to be very small because of the very large predicted ff component. On the other hand, the CN formation probability ${P}_{\mathrm{CN}}$ is found to be nearly equal to 1, and hence the decay under study is a pure CN decay for all the nuclear potentials considered, since the estimated noncompound nucleus (nCN) content is almost negligible. We have also applied the extended-Wong model of Gupta and collaborators, and find that the ${\ensuremath{\ell}}_{\mathrm{max}}$ values and total fusion cross sections are of the same order as for the DCM. Thus, the extended-Wong model, which describes only the total fusion cross section in terms of the barrier characteristics of the entrance channel nuclei, could be useful for initial experimental studies to be fully treated using the DCM for all the observed decay products.