Photoemission spectroscopy on high T_c superconductors find a puzzling nodal self-energy with ω/T scaling and an exponent varying continuously with doping. We propose a mechanism: nonlocality induced by poorly screened effective repulsions V_α(r) ∼ 1/r^α, where a continuously doping-dependent exponent 1 ≤ α ≤ 3 interpolates between the Mott insulating and Fermi liquid limits. We develop a phenomenology of hydrodynamic screening, finding a scale-covariant quasiparticle decay rate Γ(ω,T) ∝ T^γ Φ(ω/T) in energy ω and temperature T, with γ = 2-1/α for nonlocal 1 < α < 2. Our results naturally capture the optimally doped to overdoped regimes, whereas the underdoped regime is qualitatively distinct. In our theory, spectroscopy-fitted exponents directly probe the charged fluid's effective spatial nonlocality, providing a way to falsify the theory by comparing photoemission spectroscopy against electron energy loss spectroscopy. More broadly, nonlocality cautions us to not immediately infer quantum critical phenomena when ω/T scaling is experimentally observed.