Core-collapse supernovae (CCSNe) are among the most energetic processes in our Universe and are crucial for the understanding of the formation and chemical composition of the Universe. The precise measurement of the neutrino light curve from CCSNe is essential in understanding the hydrodynamics and fundamental processes that drive CCSNe. The IceCube Neutrino Observatory at the South Pole has mass-independent sensitivity within the Milky Way and some sensitivity to the higher mass CCSNe in the Large and Small Magellanic clouds. The envisaged large-scale extension of the IceCube detector, IceCube-Gen2, opens the possibility for new sensor design and trigger concepts that could increase the number of neutrinos detected from a CCSNe burst compared to IceCube. In my study, I want to investigate the prospect of IceCube-Gen2 in combination with wavelength-shifting devices for the detection of fast-time features of generic CCSN models. These studies will further inform on the scientific gains of IceCube-Gen2 and quantify the potential of wavelength-shifting technology for low-energy SN studies in IceCube.