Ultra-high-energy neutrino detectors such as ARA and RNO-G rely on radio antennas deployed in ice to detect particle cascades. In this context, the in-ice radio emission from cosmic-ray-induced particle cascades constitutes both a major background and a valuable calibration source. Accurate modeling of this emission currently relies on detailed Monte Carlo simulations, such as FAERIE, which remain computationally too expensive to efficiently explore the full parameter space. In this work, we present a semi-analytical parameterization of the in-ice radio emission from cosmic-ray showers, based on a dense library of FAERIE simulations combined with scaling laws that capture the dependence of the signal on shower parameters. This approach enables order-of-magnitude estimates of the radio signal within seconds, making it possible to generate large simulation datasets for in-ice neutrino experiments. Finally, we discuss possible approaches for mass composition reconstruction with in-ice detectors exploiting specific features of cosmic ray radio emission.