Touch gesture recognition (TGR) is essential for facilitating intuitive human-robot interaction. A range of neural network architectures, including convolutional neural networks (CNNs) and long short-term memory models, have been investigated for this purpose. Despite their effectiveness, these methods often incur substantial computational costs, limiting their suitability for deployment on mobile robotic platforms with constrained resources. Moreover, many existing lightweight approaches prioritize parameter reduction, frequently compromising overall model accuracy. Therefore, developing a compact yet high-performing framework for TGR is essential for advancing human-robot interaction. In this work, a lightweight model based on separable convolution and knowledge distillation network (CKDNet) is proposed for TGR. The model substitutes traditional 3D convolutional layers with a sequence of three one-dimensional convolutional kernels to independently capture spatial and temporal features. To further enhance recognition accuracy without compromising compactness, we incorporate a novel knowledge distillation strategy integrating feature-based and probability-based knowledge distillation. This method guides the student model, a compact separable CNN, by transferring both intermediate feature representations and output probabilities from a larger separable CNN during training. Extensive experiments on two benchmark datasets validate the effectiveness of CKDNet, demonstrating its ability to maintain a favorable trade-off between model complexity and recognition performance.