Four air-stable one-dimensional copper(II) coordination polymers (CP1-CP4) with azide linkers were synthesized using tridentate NNS and NNN ligands. Single-crystal X-ray diffraction (XRD) analysis confirmed the molecular structures of CP1, CP3, and CP4. In the presence of TEMPO, all four coordination polymers demonstrated effective catalytic activity for the selective aerobic oxidation of veratryl alcohol, a biomass model compound, under base-free conditions. CP4 exhibited the best catalytic efficiency. Oxidations were conducted at ambient temperature (40 °C) utilizing air as a sustainable oxidant. Selective oxidation of veratryl alcohol to veratraldehyde was also conducted in the presence of a catalytic amount of base (5 mol %), and enhanced reactivity was observed. The green solvents, acetone, and water, were used to maximize sustainability. The optimized reaction conditions were applied to broaden the substrate scope of various lignin model alcohols and substituted benzylic alcohols with wide electronic variability. CP4 exhibited high recyclability, consistently providing quantitative yields even after ten consecutive runs. The catalytic protocol demonstrated sustainability and environmental compatibility, as evidenced by a low E-factor (4.29) and a high Eco-scale score (90). Based on experimental evidence and theoretical calculations, a plausible catalytic cycle was proposed. Finally, the sustainability credentials of the different optimized reaction protocols were evaluated using the CHEM21 green metrics toolkit.