Although studies have demonstrated that Large Language Models (LLMs) can perform well on Out-of-Distribution (OOD) tasks, their advantage tends to diminish as the distribution shift becomes more severe. Consequently, researchers aim to retrieve distributionally similar and informative demonstrations from the available source domain to boost the inference capabilities of LLMs. However, in practical scenarios where the target domain is inaccessible, evaluating the unknown distribution is challenging, which indirectly impacts the quality of the selected demonstrations. To address this problem, we propose DOPA, a demonstration search framework that incorporates an OOD proxy to approximate the inaccessible target domain and guide the retrieval process. Building on proxy-based evaluation, DOPA further introduces a Mahalanobis distance-based global diversity constraint to ensure sufficient diversity among the retrieved demonstrations. Experimental results on multiple LLMs and tasks demonstrate that DOPA effectively enhances robustness in OOD settings.