Vision-Language Model (VLM) based retrievers have advanced visual document retrieval (VDR) to impressive quality. They require the same multi-billion parameter encoder for both document indexing and query encoding, incurring high latency and GPU dependence even for plain-text queries. We observe that this design is unnecessarily symmetric: documents are visually complex and demand strong visual understanding, whereas queries are just short text strings. NanoVDR exploits this query--document asymmetry by decoupling the two encoding paths: a frozen 2B VLM teacher indexes documents offline, while a distilled text-only student as small as 69M parameters encodes queries at inference. The key design choice is the distillation objective. Through systematic comparison of six objectives across three backbones and 22 ViDoRe benchmark datasets, we find that pointwise cosine alignment on query text consistently outperforms ranking-based and contrastive alternatives, while requiring only pre-cached teacher query embeddings and no document processing during training. Furthermore, we identify cross-lingual transfer as the primary performance bottleneck, and resolve it cheaply by augmenting training data with machine-translated queries. The resulting NanoVDR-S-Multi (DistilBERT, 69M) retains 95.1\% of teacher quality and outperforms DSE-Qwen2 (2B) on v2 and v3 with 32$\times$ fewer parameters and 50$\times$ lower CPU query latency, at a total training cost under 13 GPU-hours.