Shape Memory Alloys (SMAs) are a type of smart material that are commonly used in compact and lightweight linear actuators. Paired with compliant motion conversion mechanisms, these alloys can be transformed into lightweight grippers ideal for applications such as drone deliveries. This work proposes to use the inherent stiffness of a compliant mechanism with an SMA coil, to design and size a self-biasing SMA gripper. In this paper, with the help of 2.5D design, a functional radial 4-prong gripper is designed and fabricated. While only weighing 17g, it has a gripping force and stroke of 1.8N and 4mm, respectively. Along with this functional prototype, an analytical model and design framework is presented allowing for the design and sizing of similar self-biasing SMA actuators for other different light-weight applications.