Artificial intelligence (AI) technologies have resulted in remarkable achievements and conferred massive benefits to computer-aided systems in medical imaging. However, the worldwide usage of AI-based automation-assisted cervical cancer screening systems is hindered by computational cost and resource limitations. Thus, a highly economical and efficient model with enhanced classification ability is much more desirable. This paper proposes a hybrid loss function with label smoothing to improve the distinguishing power of lightweight convolutional neural networks (CNNs) for cervical cell classification. The results strengthen our confidence in hybrid loss-constrained lightweight CNNs, which can achieve satisfactory accuracy with much lower computational cost for the SIPakMeD dataset. In particular, ShufflenetV2 obtained a comparable classification result (96.18% in accuracy, 96.30% in precision, 96.23% in recall, and 99.08% in specificity) with only one-seventh of the memory usage, one-sixth of the number of parameters, and one-fiftieth of total flops compared with Densenet-121 (96.79% in accuracy). GhostNet achieved an improved classification result (96.39% accuracy, 96.42% precision, 96.39% recall, and 99.09% specificity) with one-half of the memory usage, one-quarter of the number of parameters, and one-fiftieth of total flops compared with Densenet-121 (96.79% in accuracy). The proposed lightweight CNNs are likely to lead to an easily-applicable and cost-efficient automation-assisted system for cervical cancer diagnosis and prevention.