Privacy-preserving crowd density analysis finds application across a wide range of scenarios, substantially enhancing smart building operation and management while upholding privacy expectations in various spaces. We propose a non-speech audio-based approach for crowd analytics, leveraging a transformer-based model. Our results demonstrate that non-speech audio alone can be used to conduct such analysis with remarkable accuracy. To the best of our knowledge, this is the first time when non-speech audio signals are proposed for predicting occupancy. As far as we know, there has been no other similar approach of its kind prior to this. To accomplish this, we deployed our sensor-based platform in the waiting room of a large hospital with IRB approval over a period of several months to capture non-speech audio and thermal images for the training and evaluation of our models. The proposed non-speech-based approach outperformed the thermal camera-based model and all other baselines. In addition to demonstrating superior performance without utilizing speech audio, we conduct further analysis using differential privacy techniques to provide additional privacy guarantees. Overall, our work demonstrates the viability of employing non-speech audio data for accurate occupancy estimation, while also ensuring the exclusion of speech-related content and providing robust privacy protections through differential privacy guarantees.