Tangible objects are used in Virtual Reality (VR) and Augmented Reality (AR) to enhance haptic information on the general shape of virtual objects. However, they are often passive or unable to simulate rich varying mechanical properties. This paper studies the effect of combining simple passive tangible objects and wearable haptics for improving the display of varying stiffness, friction, and shape sensations in these environments. By providing timely cutaneous stimuli through a wearable finger device, we can make an object feel softer or more slippery than it really is, and we can also create the illusion of encountering virtual bumps and holes. We evaluate the proposed approach carrying out three experiments with human subjects. Results confirm that we can increase the compliance of a tangible object by varying the pressure applied through a wearable device. We are also able to simulate the presence of bumps and holes by providing timely pressure and skin stretch sensations. Altering the friction of a tangible surface showed recognition rates above the chance level, albeit lower than those registered in the other experiments. Finally, we show the potential of our techniques in an immersive medical palpation use case in VR. These results pave the way for novel and promising haptic interactions in VR, better exploiting the multiple ways of providing simple, unobtrusive, and inexpensive haptic displays.