The decay of 28Si⁎ compound system formed by 12C+16O reaction is analyzed at stellar energies span Ec.m. = 4 - 5 MeV. The conventional SIII Skyrme force is used in conjunction with generalized GSkI and extended eMSL07 Skyrme forces having extended density-dependent terms, that can be potentially useful for the study of finite nuclei and the neutron stars. The dynamical cluster-decay model (DCM) is used to examine the emission of n, p, and α particles in the decay of 28Si⁎ nucleus along with other competing decay channels. The theoretical analysis advocates the emergence of 6Li, 10B, and 14N fragments in the decay of 28Si⁎ nucleus, independent of the choice of Skyrme interactions and the angular momentum effects. The fragile nature of 6Li nucleus may not allow it to survive the stellar conditions and hence the breakup and /or radiative capture processes may appear in. The breakup of L6i is addressed in terms of Kinetic energy (K.E) value of A=6 fragment while the possibility of capture reaction is predicted in terms of positive Q values of radiative capture reactions 6Li(n,γ)7Li, 6Li(p,γ)7Be, and 6Li(α,γ)10B. It has been observed that the structure of fragmentation potential and preformation probability is independent of the choice of Skyrme forces, but their magnitude gets significantly influenced for use of different Skyrme forces. The conventional SIII force could not reproduce the cross sections while eMSL07 and GSkI Skyrme forces give nice agreement with the experimental data.