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We report detailed investigation of diamond-on-silica waveguides and their potential for use as Raman lasers. Large cross-sectional area rib waveguides are proposed as a dimension-scalable geometry. Finite element analysis and the beam propagation method are used to assess their guiding properties and in particular single transverse mode operation. A fully analytical model of scattering losses taking into account the interaction with all surfaces is proposed and exploited in conjunction with an analytical solution of a Raman waveguide laser to optimize the design with respect to threshold or output power of a diamond Raman waveguide laser pumped continuous-wave either at 532 nm or 1064 nm. Results show that thresholds lower than 500 mW and near quantum limit output powers can be obtained for a range of guide dimensions.