In this paper, we present a hardware-control co-design approach that enables efficient and versatile roller skating on quadrupedal robots equipped with passive wheels. Passive-wheel skating reduces leg inertia and improves energy efficiency, particularly at high speeds. However, the absence of direct wheel actuation tightly couples mechanical design and control. To unlock the full potential of this modality, we formulate a bilevel optimization framework: an upper-level Bayesian Optimization searches the mechanical design space, while a lower-level Reinforcement Learning trains a motor control policy for each candidate design. The resulting design-policy pairs not only outperform human-engineered baselines, but also exhibit versatile behaviors such as hockey stop (rapid braking by turning sideways to maximize friction) and self-aligning motion (automatic reorientation to improve energy efficiency in the direction of travel), offering the first system-level study of dynamic skating motion on quadrupedal robots.