Humans rely on multimodal perception to form representations of the world. This implies that environmental stimuli must remain consistent and predictable throughout their journey to our sensory organs. When it comes to vision, electromagnetic waves are minimally affected when passing through air or glass treated for chromatic aberrations. Similar conclusions can be drawn for hearing and acoustic waves. However, tools that propagate elastic waves to our cutaneous afferents tend to color tactual perception due to parasitic mechanical attributes such as resonances and inertia. These issues are often overlooked, despite their critical importance for haptic devices that aim to faithfully render or record tactile interactions. Here, we investigate how to optimize this mechanical transmission with sandwich structures made from rigid, lightweight carbon fiber sheets arranged around a 3D-printed lattice core. Through a comprehensive parametric evaluation, we demonstrate how this design paradigm provides superior haptic transparency, regardless of the lattice types. Drawing an analogy with topology optimization, our solution approaches a foreseeable technological limit. It offers a practical way to create high-fidelity haptic interfaces, opening new avenues for research on tool-mediated interactions.