Wearable haptic devices in the shape of actuated thimbles are used to render the sense of touch in teleoperation and virtual reality scenarios. The design of similar devices has to comply with concurring requirements and constraints: lightweight and compactness, intensity and bandwidth of the rendered signals. Micro-sized motors require a mechanical reduction to increase the output force, at the cost of noise and vibrations introduced by conventional gear reducers. Here we propose a different actuation method, based on a miniaturized twisted string actuator and a flexure hinge transmission mechanism. The latter is required to transmit and transform the pulling force of the twist actuator to a pushing force of the plate in contact with the fingerpad. It achieves a lightweight and noiseless actuation in a compact mechanism. In this work, we present design guidelines of the proposed approach, optimization, and FEM analysis of the flexure hinge mechanism, implementation of the prototype, and experimental characterization of the twist actuator measuring frequency response and output force capabilities.