Interest in soft robotics has increased in recent years due to their potential in a myriad of applications. A wide variety of soft robots has emerged, including bio-inspired robotic swimmers such as jellyfish, rays, and robotic fish. However, the highly nonlinear fluid-structure interactions pose considerable challenges in the analysis, modeling, and feedback control of these soft robotic swimmers. In particular, developing models that are of high fidelity but are also amenable to control for such robots remains an open problem. In this work, we propose a data-driven approach that exploits Koopman operators to obtain a linear representation of the soft swimmer dynamics. Specifically, two methodologies are explored for obtaining the basis functions of the the operator, one based on data-based derivatives estimated using high-gain observers, and the other based on the dynamics structure of a tail-actuated rigid-body robotic fish. The resulting approximate finite-dimensional operators are trained and evaluated using data from high-fidelity CFD simulations that incorporate fluid-structure interactions. Validation results demonstrate that, while both methods are promising in producing control-oriented models, the approach based on derivative estimates shows higher accuracy in state prediction.