Over the last decades, a range of flexible cables such as the Flexible Flat Cables (FFC) have become very popular in the electronics industry, as they have been used to connect various electronic components in consumer devices (e.g., smartphones, laptops, tables etc.). The assembly of such flexible cables is typically accomplished by highly trained workers that perform repetitive tasks, or by simple robotic mechanisms that rely on clamping structures and/or on suction cups. But human workers get easily tired and need breaks while the simple, rigid robotic devices lack the required dexterity for robotic manipulation, are difficult to program, rely on sophisticated sensing, and require complicated control laws. In this work, we focus on the robotic manipulation of a plethora of flexible cables, proposing a multi-modal gripper with locally-dexterous tips and active fingernails. The fingers of the gripper are equipped with: i) self-aligning structures that conform to the object shape maximizing grasping stability, ii) locally-dexterous fingertips that accommodate manipulation-capable degrees of freedom, and iii) a combination of Nitinol-based active fingernails and suction cups that allow picking up and handling of cables that rest on flat surfaces. The proposed robotic gripper is equipped with a camera and a perception system that allow for the execution of complex cable manipulation and assembly tasks in dynamic environments.