Robust speech recognition systems rely on cloud service providers for inference. It needs to ensure that an untrustworthy provider cannot deduce the sensitive content in speech. Sanitization can be done on speech content keeping in mind that it has to avoid compromising transcription accuracy. Realizing the under utilized capabilities of tiny speech foundation models (FMs), for the first time, we propose a novel use: enhancing speech privacy on resource-constrained devices. We introduce SpeechShield, an edge/cloud privacy preserving speech inference engine that can filter sensitive entities without compromising transcript accuracy. We utilize a timestamp based on-device masking approach that utilizes a token to entity prediction model to filter sensitive entities. Our choice of mask strategically conceals parts of the input and hides sensitive data. The masked input is sent to a trusted cloud service or to a local hub to generate the masked output. The effectiveness of SpeechShield hinges on how well the entity time segments are masked. Our recovery is a confidence score based approach that chooses the best prediction between cloud and on-device model. We implement SpeechShield on a 64 bit Raspberry Pi 4B. Experiments show that our solution leads to robust speech recognition without forsaking privacy. SpeechShield with < 100 MB memory, achieves state-of-the-art (SOTA) speech transcription performance while filtering about 83% of private entities directly on-device. SpeechShield is 16x smaller in memory, 3.3x faster and 17x more compute efficient than prior privacy preserving speech frameworks and has a relative reduction in word error rate (WER) by 38.8-77.5% when compared to existing offline transcription services.