We introduce a versatile, easy-to-implement Gaussian process model that provides a flexible framework for modeling core-radius fluctuations of an optical fiber. The flexibility of the model allows for easy modification of the fiber profile to fit known characteristics, such as forcing the profile through carefully measured radii at specific points. The model is then used to show the drastic impact that fluctuations have on the efficiency of wide-spanning four-wave mixing systems. Furthermore, by optimizing the fiber design of a simple step-index fiber, we show that the efficiency of the four-wave mixing can be drastically improved even in the presence of large core-radius fluctuations.