On-chip hollow-core waveguides enable strong light-matter interaction in gases and liquids with high integration density, yet limited side access to the core restricts their use in diffusion-driven processes. We introduce a distinct class of on-chip hollow-core waveguides that confines light in a scaffold membrane geometry composed predominantly of air, reaching claddingopenness fraction up to 80% while maintaining optical losses comparable to fully enclosed waveguides. Light guidance in the photonic scaffold is enabled by the combination of anti-resonant confinement with Bloch-mode formation in a segmented structure. High-precision 3D nanoprinting, extensive optical characterization and a resonator-based theoretical model confirm the guiding principle and loss behavior. We demonstrate application relevance through enhanced molecular diffusion, highly integrated optofluidic spectroscopy, and efficient single-photon transmission enabled by the open scaffold geometry and air-dominant guidance.