Near-infrared wavefront sensing allows for the enhancement of sky coverage with adaptive optics. The recently developed HgCdTe avalanche photodiode arrays are promising due to their very low detector noise, but still present an imperfect cosmetic that may directly impact real-time wavefront measurements for adaptive optics and thus degrade performance in astronomical applications. We propose here a model of a Shack-Hartmann wavefront measurement in the presence of residual fixed pattern noise and defective pixels. To adjust our models, a fine characterization of such an HgCdTe array, the RAPID sensor, is proposed. The impact of the cosmetic defects on the Shack-Hartmann measurement is assessed through numerical simulations. This study provides both a new insight on the applicability of cadmium mercury telluride (CMT) avalanche photodiodes detectors for astronomical applications and criteria to specify the cosmetic qualities of future arrays.