To wield an object means to hold and move it in a way that exploits its functions. When we wield tools -- such as writing with a pen or cutting with scissors -- our hands would reach very specific poses, often drastically different from how we pick up the same objects just to transport them. In this work, we investigate the design of tool-wielding multi-finger robotic hands based on a hypothesis: the poses that a tool and a hand reach during tool-wielding -- what we call "foundational poses" (FPs) -- can be used as a selection mechanism in the design process. We interpret FPs as snapshots that capture the workings of underlying mechanisms formed by the tool and the hand, and one hand can form multiple mechanisms with the same tool. We tested our hypothesis in a hand design experiment, where we developed a sampling-based design optimization framework that uses FPs to computationally generate many different hand designs and evaluate them in multiple metrics. The results show that more than $99\%$ of the $10,785$ generated hand designs successfully wielded tools in simulation, supporting our hypothesis. Meanwhile, our methods provide insights into the non-convex, multi-objective hand design optimization problem that could be hard to unveil otherwise, such as clustering and the Pareto front. Lastly, we demonstrate our methods' real-world feasibility and potential with a hardware prototype equipped with rigid endoskeleton and soft skin.