I responded to a similar question a few months ago thusly:

Commodore Perry had done his research before departing on his mission, and had prepared for negotiation with Japan in a few likely formats.

The official interpreter of the Perry mission was a man named Samuel Wells Williams, who had a rather unique back story (Sinologist, missionary to China, publisher, member of a failed prior expedition to Japan). Williams was not confident of his limited command of Japanese, built entirely upon conversations with shipwrecked Japanese sailors. But he had excellent command of Mandarin Chinese, which was thought as one possible option for official dialogue. In fact when they arrived in Japan, it was the Japanese use of Dutch, rather than Mr. Williams' familiarity with Japanese and Chinese, which would form the basis of their negotiations. From Williams' diary of the events:

"During the whole of this interview the bearing of these Japanese was dignified and self-possessed. Yezaimon spoke in a clear voice and, through Tatsnoski, who put it into Dutch for Mr. Portman, I could make out almost all they said; but it would require considerable practice to speak that style, and I am not sorry that one of them knows Dutch so much better than I do Japanese, for I think intercommunication is likely to be more satisfactory."

"Mr. Portman" referenced above was Anton Portman, a Dutch civilian brought along on the mission because it was known that some Japanese could speak Dutch.

Rather than being a fortunate coincidence that the mission happened upon Japanese officials who spoke Dutch, it soon became clear that officials of the Japanese government meant to use Dutch exclusively in conducting verbal negotiations. Official documents, however, were to be written in Chinese.

In these written documents, Chinese played an important role as a kind of legal lingua franca. Each side would write first in their primary language (English and Japanese respectively), then translate the respective document into Chinese. The two sides would then negotiate, making requisite corrections to the Chinese document. Once a final version was agreed upon they would make additional copies in Dutch and English (for the Americans,) and Dutch and Japanese (for the Japanese).

EDIT: Incidentally, here's a link to Samuel Williams' journal of his experiences on the Perry mission. It makes for fun reading. For unknown reasons he was the only participant of the mission allowed to publish such a journal without prior approval from Commodore Perry. That lends it a refreshingly candid quality.