Oceans are harsh environments and can impose significant loads on deployed structures. The deployment of wave energy converters (WECs) faces a design challenge with apparently contradictory goals. A WEC should be designed to maximize the energy absorbed while ensuring the operating wave condition does not exceed the failure limits of the device itself. Therefore, the loads endured by the support structure are a design constraint for the system. Adaptability to different sea states is, therefore, highly desirable. This work uses a WEC-Sim model of a variable-geometry oscillating wave energy converter (VGOSWEC) mounted on a support structure simulated under different wave scenarios. A VGOSWEC resembles a paddle pitching about a fixed hinge perpendicular to the incoming wave fronts. Therefore, the hinge experiences loads perpendicular to its axis as it maintains its position. The geometry of the VGOSWEC is varied by opening a series of controllable flaps on the pitching paddle when the structure experiences threshold loads. Because opening the flaps lets the waves transmit through the paddle, it is hypothesized that opening the flaps should result in load shedding at the base of the support structure. The load shedding is achieved by reducing the moments about the hinge axis. This work compares the hydrodynamic coefficients, natural periods, and response amplitude operators from completely closed to completely open configurations of the controllable flaps. The comparisons quantify the effects of letting the waves transmit through the VGOSWEC. This work shows that the completely open configuration can reduce the pitch and surge loads on the base of the support structure by as much as 80%. It was observed that at the paddle’s resonance frequency, the loads on the structure increased substantially. This increase in loads can be mitigated by a rotational power take-off damping about the hinge axis. Changing the rotational power take-off damping was identified as an additional design parameter that can be used to control the loads experienced by the WEC’s support structure.