In this paper, we investigate the reconstruction of hydrodynamic forces and torques, as well as the fluid velocity profile along the body of a swimmer in a Kármán Vortex Street (KVS) through data-driven methods. We collect hydrodynamic data from a high-fidelity Computational Fluid Dynamic (CFD) simulation of the swimmer, and construct a latent data-driven model through Principal Component Analysis (PCA). We generate optimal sensor positions through a QR decomposition of the latent space, allowing us to identify non-trivial sensor positions that hold the most information about the PCA latent variables. We use the measurements from the sparse set of optimal sensors, in conjunction with the PCA model to reconstruct the latent variables, and subsequently the features in the data which are not measured, resulting in a computationally efficient method. We demonstrate the method in two applications: recovering forces and torques, and estimating the speed profile of the fluid along the boundary of the swimmer.