This work presents HapticSphere, a wearable spherical surface enabled by bridging a finger and the head-mounted display (HMD) with a passive string. Users perceive a physical support on a finger attached to a string, when extending their arm and reaching out to the string's maximum extension. This physical support assists users in precise touch interaction in the context of stationary and walking virtual or mixed-reality experiences. We propose three methods of attachment of the haptic string (directly on the head or on the body), and illustrate a novel single-step calibration algorithm that supports these configurations by estimating a grand haptic sphere, once a head-coordinated touch interaction is established. Two user studies were conducted to validate our approach and to compare the touch performance with physical support in sitting and walking conditions in the context of mobile mixed-reality scenarios. The results show that, in the walking condition, touch interaction with physical support significantly outperformed the visual-only condition.