As plots play a critical role in modern data visualization and analysis, Plot2API is launched to help non-experts and beginners create their desired plots by directly recommending graphical APIs from reference plot images by neural networks. However, previous works on Plot2API have primarily focused on the recommendation for standard plot images, while overlooking the hand-drawn plot images that are more accessible to non-experts and beginners. To make matters worse, both Plot2API models trained on standard plot images and powerful multi-modal large language models struggle to effectively recommend APIs for hand-drawn plot images due to the domain gap and lack of expertise. To facilitate non-experts and beginners, we introduce a hand-drawn plot dataset named HDpy-13 to improve the performance of graphical API recommendations for hand-drawn plot images. Additionally, to alleviate the considerable strain of parameter growth and computational resource costs arising from multi-domain and multi-language challenges in Plot2API, we propose Plot-Adapter that allows for the training and storage of separate adapters rather than requiring an entire model for each language and domain. In particular, Plot-Adapter incorporates a lightweight CNN block to improve the ability to capture local features and implements projection matrix sharing to reduce the number of fine-tuning parameters further. Experimental results demonstrate both the effectiveness of HDpy-13 and the efficiency of Plot-Adapter.