The development of the field of soft robotics has led to the exploration of novel techniques to manufacture soft actuators, which provide distinct advantages for wearable assistive robotics. One subset of these soft pneumatic actuators is conventionally developed from silicone, fabrics, and thermoplastic polyurethane (TPU). Each of these materials in isolation possesses limitations of low-stress capacity, low-design complexity, and high-input pressure requirements, respectively. Combining these materials can overcome some limitations and maintain their desirable properties. In this article, we explore one such composite design scheme using a combination of silicone polymer-based bladder and reconfigurable fabric skin made from an anisotropic extensible fabric. The silicone polymer bladder acts as the hermetic seal, while this skin acts as the constraint. Bending and torsional actuators were designed utilizing the anisotropy of these fabrics. The torsional actuator designs can achieve over 540° of twist, significantly larger than previously reported in the literature, owing to the lower mechanical impedance of the extensible fabrics. Actuators with 360° of bending were also fabricated using this method. In addition, the lack of TPU-backed or inextensible fabrics reduces the actuator's stiffness, leading to lower actuation pressures. Skin-based designs also confer the advantage of modularity, reconfigurability, and the ability to achieve complex motions by tuning the properties of the bladder and the skin. For applications with high-force requirements, such as wearable exoskeletons, we demonstrate the utility of multilayer design schemes. A multilayer bending actuator generated 190 N of force at 100 kPa and was shown to be a candidate for wearable assistive devices. In addition, torsional designs were shown to have utility in practical scenarios such as screwing on a bottle cap and turning knobs. Thus, we present a novel fabric-skin-based design concept that is highly versatile and customizable for various application requirements.