Contrastive vision-language models have achieved remarkable progress through large-scale pretraining. Recent work has shown that removing English-only caption filters and pretraining on global data is effective for improving multicultural performance. We study whether such global pretraining is sufficient for culture-specific understanding, or whether further adaptation with natively sourced data can boost performance beyond what global pretraining alone achieves. To enable this investigation, we present WAON, the largest publicly available native Japanese image-text dataset constructed from native Japanese web content in Common Crawl, containing approximately 155 million examples. We also introduce WAON-Bench, a manually curated Japanese cultural benchmark spanning 374 classes. Through comparative fine-tuning experiments on multiple Japanese image-text datasets, we observe that models fine-tuned on WAON consistently achieve stronger performance on Japanese cultural benchmarks than those fine-tuned on English-to-Japanese translated data. We release our dataset and code.