This paper presents HaptiCraft, a modular handheld haptic controller designed to replicate the appearance, mass distribution, and multimodal haptic properties of virtual objects. HaptiCraft consists of many modules that provide distinct functions for assembly and multimodal haptic feedback, supporting five types: vibration, impact, thermal, variable inertia, and variable stiffness. Users can readily assemble these modules to create a controller tailored to their needs. To simplify the design process, especially for novice users, we also provide a graphical authoring tool and assess its usability. Finally, we evaluate the system's effectiveness through various virtual reality (VR) scenarios, demonstrating that HaptiCraft significantly enhances user experience. HaptiCraft makes a substantial contribution to the field of VR handheld controllers by offering comprehensive support for shape-changing, variable inertia, and rich multimodal haptic feedback, coupled with an effective authoring method.