Distributionally robust optimization (DRO) is a mathematical framework to incorporate ambiguity over the actual data-generating probability distribution. Data-driven DRO problems based on the Wasserstein distance are of particular interest for its sound mathematical properties. For right-hand-sided uncertainty however, existing methods rely on dual vertex enumeration rendering the problem intractable in practical applications. In this context, we study decomposition methods for two-stage data-driven Wasserstein-based DROs with right-hand-sided uncertainty and rectangular support. We propose a novel finite reformulation that explores the rectangular uncertainty support to develop and test three new different decomposition schemes: Column-Constraint Generation, Single-cut Benders and Multi-cut Benders. We compare the efficiency of the proposed methods with an existing benchmark for a unit commitment problem with 5, 14, and 54 thermal generators over a 24-hour uncertainty dimension.