In realistic speech enhancement settings for end-user devices, we often encounter only a few speakers and noise types that tend to reoccur in the specific acoustic environment. We propose a novel personalized speech enhancement method to adapt a compact denoising model to the test-time specificity. Our goal in this test-time adaptation is to utilize no clean speech target of the test speaker, thus fulfilling the requirement for zero-shot learning. To complement the lack of clean utterance, we employ the knowledge distillation framework. Instead of the missing clean utterance target, we distill the more advanced denoising results from an overly large teacher model, and use it as the pseudo target to train the small student model. This zero-shot learning procedure circumvents the process of collecting users' clean speech, a process that users are reluctant to comply due to privacy concerns and technical difficulty of recording clean voice. Experiments on various test-time conditions show that the proposed personalization method achieves significant performance gains compared to larger baseline networks trained from a large speaker- and noise-agnostic datasets. In addition, since the compact personalized models can outperform larger general-purpose models, we claim that the proposed method performs model compression with no loss of denoising performance.