As virtual objects contain increasingly rich attribute information, small wearable fingertip devices need to have higher degrees of freedom (DoFs) to convey the haptic sensation of virtual objects. In order to effectively display the shape features of virtual objects to users through curvature, we designed a 6-DoF wearable fingertip device (WFD). This WFD combines a 6-DoF Stewart parallel mechanism, consisting of a static platform and a mobile platform connected by six revolute-spherical-spherical kinematic chains. The translation and rotation of the mobile platform are driven by six miniature servo motors, which can simulate haptic sensations such as making and breaking contact, sliding, and skin stretch when the fingertip interacts with a virtual surface. The WFD is fixed at the user's dominant index finger using hook-and-loop fasteners, with a size of 68 × 59 × 56 mm$^{3}$3 and a mass of 45.5 g. We analyzed and validated the kinematic model of the WFD and tested its force output capability. Finally, we invited 15 adults to conduct three subjective perception experiments to evaluate the performance of the WFD in curvature perception and shape display. The experimental results show that: (1) The just noticeable difference (JND) for curvature identification using the WFD is 3.02$\pm$±0.23 m$^{-1}$-1; (2) The 6-DoF haptic feedback provided by the WFD improves the accuracy of curved surface recognition from 53.4$\pm$±7.1% in 3-DoF to 72.0$\pm$±5.9%; (3) Even without visual feedback, the shape recognition accuracy of the WFD when combined with the Touch device reaches 82.3$\pm$±8.2% . Experimental results show that the WFD has good performance and potential in curvature perception and shape display.