Speech recognition performance varies by language, domain, and speaker characteristics such as accent, but fine-tuning a model on any of these categories may lead to catastrophic forgetting. Token-level $k$ nearest neighbor search ($k$NN), first proposed for neural sequence decoders for natural language generation (NLG) and machine translation (MT), is a non-parametric method that instead adapts using inference-time search in an external datastore, without training the underlying model. We show that Whisper, a transformer end-to-end speech model, benefits from $k$NN. We investigate the differences between the speech and text setups. We discuss implications for speaker adaptation, and analyze improvements by gender, accent, and age.