We discuss a probe of the contribution of wind-related shocks to the radio emission in otherwise radio-quiet quasars. Given (1) the nonlinear correlation between UV and X-ray luminosity in quasars, (2) that such a correlation leads to higher likelihood of radiation-line-driven winds in more luminous quasars, and (3) that luminous quasars are more abundant at high redshift, deep radio observations of high-redshift quasars are needed to probe potential contributions from accretion disk winds. We target a sample of 50 z~1.65 color-selected quasars that span the range of expected accretion disk wind properties as traced by broad CIV emission. 3GHz observations with the Very Large Array to an rms of ~10{mu}Jy/beam probe to star formation rates of ~400M{sun}/yr, leading to 22 detections. Supplementing these pointed observations are survey data of 388 sources from the LOFAR Two-meter Sky Survey Data Release 1 that reach comparable depth (for a typical radio spectral index), where 123 sources are detected. These combined observations reveal a radio detection fraction that is a nonlinear function of CIV emission-line properties and suggest that the data may require multiple origins of radio emission in radio-quiet quasars. We find evidence for radio emission from weak jets or coronae in radio-quiet quasars with low Eddington ratios, with either (or both) star formation and accretion disk winds playing an important role in optically luminous quasars and correlated with increasing Eddington ratio. Additional pointed radio observations are needed to fully establish the nature of radio emission in radio-quiet quasars.