Recent advances in automatic speech recognition (ASR) often rely on large speech foundation models for generating high-quality transcriptions. However, these models can be impractical due to limited computing resources. The situation is even more severe in terms of more realistic or difficult scenarios, such as code-switching ASR (CS-ASR). To address this, we present a framework for developing more efficient models for CS-ASR through knowledge distillation using realistic speech-only data. Our proposed method, Leave No Knowledge Behind During Knowledge Distillation (K$^2$D), leverages both the teacher model's knowledge and additional insights from a small auxiliary model. We evaluate our approach on two in-domain and two out-domain datasets, demonstrating that K$^2$D is effective. By conducting K$^2$D on the unlabeled realistic data, we have successfully obtained a 2-time smaller model with 5-time faster generation speed while outperforming the baseline methods and the teacher model on all the testing sets. We have made our model publicly available on Hugging Face (https://huggingface.co/andybi7676/k2d-whisper.zh-en).