In the post-COVID-19 world, radio frequency (RF)-based noncontact methods, for example, software-defined radios (SDRs)-based methods, have emerged as promising candidates for intelligent remote sensing of human vitals and could help in the containment of contagious viruses like COVID-19. To this end, this work utilizes the universal software radio peripherals (USRPs)-based SDRs along with classical machine-learning (ML) methods to design a noncontact method to monitor different breathing abnormalities. Under our proposed method, a subject rests his/her hand on a table in between the transmit and receive antennas, while an orthogonal frequency division multiplexing (OFDM) signal passes through the hand. Subsequently, the receiver extracts the channel frequency response (CFR) [basically, fine-grained wireless channel state information (WCSI)] and feeds it to various ML algorithms that eventually classify between different breathing abnormalities. Among all classifiers, the linear support vector machine (SVM) classifier resulted in a maximum accuracy of 88.1% To train the ML classifiers in a supervised manner, data were collected by doing real-time experiments on four subjects in a laboratory environment. For the label-generation purpose, the breathing of the subjects was classified into three classes: normal, fast, and slow breathing. Furthermore, in addition to our proposed method (where only a hand is exposed to RF signals), we also implemented and tested the state-of-the-art method (where a full chest is exposed to RF radiation). The performance comparison of the two methods reveals a tradeoff, that is, the accuracy of our proposed method is slightly inferior but our method results in minimal body exposure to (nonionizing) RF radiation, compared to the benchmark method.