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 crucial to understanding the hydrodynamics and fundamental processes that drive CCSNe. The IceCube Neutrino Observatory 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 this contribution, we study how wavelength-shifting technology can be used in IceCube-Gen2 to measure the fast modulations of the neutrino signal due to standing accretion shock instabilities (SASI).