In this study, the advanced manipulability of wave functions in a type-II multi-shell hetero-nanostructure (MS-HNS) and the tunability of radiative exciton lifetime over a wide range with and/or without changing in transition energies has been demonstrated by the band edge engineering. For this purpose, the electronic and optical properties of exciton (X) and biexciton (XX) in a spherical CdS/ZnSe/ZnTe/CdSe HNS have been explored in detail. In the calculations, effects of all Coulombic interactions between the charges have been taken into account on the wave functions. Moreover, in the case of XX, the exchange-correlation potential between the same charged particles has also been considered. The results have been presented as a function of CdS core radius and ZnSe shell thickness and the probable physical reasons have been discussed in detail.