Smaller machine learning models, with less complex architectures and sensor inputs, can benefit wearable sensor-based human activity recognition (HAR) systems in many ways, from complexity and cost to battery life. In the specific case of smart factories, optimizing human-robot collaboration hinges on the implementation of cutting-edge, human-centric AI systems. To this end, workers' activity recognition enables accurate quantification of performance metrics, improving efficiency holistically. We present a two-stage semantic-aware knowledge distillation (KD) approach, TSAK, for efficient, privacy-aware, and wearable HAR in manufacturing lines, which reduces the input sensor modalities as well as the machine learning model size, while reaching similar recognition performance as a larger multi-modal and multi-positional teacher model. The first stage incorporates a teacher classifier model encoding attention, causal, and combined representations. The second stage encompasses a semantic classifier merging the three representations from the first stage. To evaluate TSAK, we recorded a multi-modal dataset at a smart factory testbed with wearable and privacy-aware sensors (IMU and capacitive) located on both workers' hands. In addition, we evaluated our approach on OpenPack, the only available open dataset mimicking the wearable sensor placements on both hands in the manufacturing HAR scenario. We compared several KD strategies with different representations to regulate the training process of a smaller student model. Compared to the larger teacher model, the student model takes fewer sensor channels from a single hand, has 79% fewer parameters, runs 8.88 times faster, and requires 96.6% less computing power (FLOPS).