Hadronic electromagnetic form factors and radiative decay properties offer a crucial window into the nonperturbative dynamics of quantum chromodynamics (QCD). In this work, we employ the light-cone sum rules (LCSR) method to systematically investigate the M1 radiative decay of vector mesons. Our study covers processes including $K^{*-}\to K^{-}\gamma$, $D^{*}\to D\gamma$, $B^{*}\to B\gamma$, $D_s^{*+}\to D_s^{+}\gamma$, and $B_s^{*}\to B_s\gamma$, and further extends to the excited charmonium state $\psi (2S)$. Our calculations yield decay widths for $K^{*}$ and $\psi (2S)$ that are in excellent agreement with experimental data. For the charm and bottom meson decays, where precise measurements are lacking, we provide theoretical predictions and compare them with other theoretical approaches. Most notably, our analysis reveals a universal linear dependence of the decay width on a function A(x) in the logarithmic coordinate system, which originates from the two-body decay dynamics and the ratio of the initial and final state decay constants. This relationship holds for the ground state $V\to P\gamma$ processes here and suggests a broader applicability to radiative decays of ground-state vector mesons.