Human activities within smart infrastructures generate a vast amount of IMU data from the wearables worn by individuals. Many existing studies rely on such sensory data for human activity recognition (HAR); however, one of the major bottlenecks is their reliance on pre-annotated or labeled data. Manual human-driven annotations are neither scalable nor efficient, whereas existing auto-annotation techniques heavily depend on video signatures. Still, video-based auto-annotation needs high computation resources and has privacy concerns when the data from a personal space, like a smart-home, is transferred to the cloud. This paper exploits the acoustic signatures generated from human activities to label the wearables' IMU data at the edge, thus mitigating resource requirement and data privacy concerns. We utilize acoustic-based pre-trained HAR models for cross-modal labeling of the IMU data even when two individuals perform simultaneous but different activities under the same environmental context. We observe that non-overlapping acoustic gaps exist with a high probability during the simultaneous activities performed by two individuals in the environment's acoustic context, which helps us resolve the overlapping activity signatures to label them individually. A principled evaluation of the proposed approach on two real-life in-house datasets further augmented to create a dual occupant setup, shows that the framework can correctly annotate a significant volume of unlabeled IMU data from both individuals with an accuracy of $\mathbf{82.59\%}$ ($\mathbf{\pm 17.94\%}$) and $\mathbf{98.32\%}$ ($\mathbf{\pm 3.68\%}$), respectively, for a workshop and a kitchen environment.