Scalable local control over gate operations is an outstanding challenge in the field of quantum computing and programmable quantum simulation with Rydberg-atom arrays. One approach is to use a global field to excite atoms to the Rydberg state and tune individual atoms in and out of resonance via local light shifts. In this work, we point out that photon-scattering errors from light shifts can be significantly reduced if the light shift is applied to the Rydberg state instead of the ground state, which can be realized in Rydberg states of alkaline-earth atoms using optical transitions in the ion core. As a proof of concept, we experimentally demonstrate global control of Rydberg excitations in an Yb optical-tweezer array via light shifts induced by a laser tuned near the Yb^{+}6s→6p_{1/2} transition. We also perform detailed spectroscopy of the induced light shift and scattering rates of the 6sns^{3}S_{1} Rydberg states and reveal the existence of satellite lines where losses from autoionization are strongly suppressed. This work can be readily extended to implement local gate operations in Rydberg-atom arrays.