We theoretically investigate and optimize four-wave mixing (FWM) in silicon nitride (SiN) waveguides integrated with two-dimensional (2D) layered graphene oxide (GO) films. Based on extensive previous measurements of the material parameters of the GO films, we perform detailed analysis for the influence of device parameters including waveguide geometry, GO film thickness, length, and coating position on the FWM conversion efficiency (CE) and conversion bandwidth (CB). The influence of dispersion and photo-thermal changes in the GO films is also discussed. Owing to the strong mode overlap between the SiN waveguides and the highly nonlinear GO films, FWM in the hybrid waveguides can be significantly enhanced. We obtain good agreement with previous experimental results and show that by optimizing the device parameters to balance the trade-off between Kerr nonlinearity and loss, the FWM CE can be improved by as much as ~20.7 dB and the FWM CB can be increased by ~4.4 folds, relative to the uncoated waveguides. These results highlight the significantly enhanced FWM performance that can be achieved in SiN waveguides by integrating 2D layered GO films.