Private conversations in social Virtual Reality (VR) environments lack the nuanced cues of physical interactions, potentially diminishing the sense of privacy and social presence. This paper introduces Whisper, a novel multisensory interaction technique designed to enhance private conversations for social VR applications. We first conducted a formative study (N = 20) to understand private conversation demands, limitations of existing methods, and user expectations in social VR. Informed by these insights, Whisper incorporates visual (avatar proximity, gestures and illumination), auditory (voice conversation), and tactile (simulated airflow) elements to simulate the act of whispering, providing users with an intuitive and immersive method of private communication. The technique also features a contextual record to maintain conversation continuity. We evaluated Whisper through a comparative user study (N = 24) in party and classroom scenarios. Results demonstrate that Whisper significantly outperforms existing methods in sense of privacy, mode distinguishability, intimacy, perceptual realism, and social presence.