In emerging and future shared-spectrum wireless networks like Citizens Broadband Radio Service (CBRS), the ability to detect radar signals without assistance from the radar transmitter is of paramount importance. This paper presents RadYOLOLet, a novel supervised deep learning-based spectrum sensing approach designed to detect low-power radar signals in the presence of interference and estimate the radar signal parameters. RadYOLOLet employs two independently trained convolutional neural networks, RadYOLO and Wavelet-CNN. RadYOLO operates on spectrograms and provides most of the capabilities of RadYOLOLet unless the signal-to-noise-and-interference ratio (SINR) is very low. In such cases, Wavelet-CNN is utilized to operate on the continuous wavelet transform of the captured signals, enhancing the detection outcome. The performance of RadYOLOLet is evaluated through various experiments using different types of interference signals. The results indicate that RadYOLOLet maintains accurate radar detection performance for SINRs of 16 dB or higher for all five types of radar signals considered, which surpasses the capabilities of other comparable methods.