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We propose and theoretically investigate chalcogenide waveguide as a more energy-efficient platform than silicon waveguide for coherent anti-Stokes Raman scattering (CARS)-based wavelength conversion. 5.5-dB Stokes to anti-Stokes conversion efficiency is observed in an As2Se3 waveguide Raman wavelength converter, which is more than 10 dB higher than its silicon counterpart. Meanwhile, dispersion engineering is discussed for As2Se3 waveguide, in which the normal material dispersion can be solely compensated by waveguide dispersion in the 1550-nm wavelength band. It is found that a nonlinear dynamic phase shift causes significant fluctuation from the perfect phase-matching condition in the As2Se3 waveguide Raman wavelength converter, highlighted by a 20-dB efficiency reduction when the pump power is high. This is due to the comparable Raman and electronic susceptibility in As2Se3 waveguide. In addition, we explore the characteristics of the CARS process in the weak pump regime for the first time according to our knowledge. Such a scheme results in simultaneous anti-Stokes wavelength generation and signal depletion, which is critical for specific applications such as intensity modulation through pulse erasure. Conversion efficiency is much lower in the weak pump region, influenced by both signal and Stokes pump power. Signal depletion ratio up to 78% can be achieved.