Depends. He probably would just write about it in the language he knows, so as not to confuse the reader. If he KNOWS any of the slang at the time, he might use that.

You might want to check out a few of the more diplomatic passages in Herodotus' Historiae (I'd recommend the passages about Gelon, Athens/Sparta and similar). He aims at what for his time is relatively reliable information (hearsay, self observation and dialogue re-construction) and he provides every scrap of information he can get his hands on.

But the point is, most of the dialogue he uses is dialogue he has had to reconstruct. There might be documents detailing what was said during official diplomatic missions, but not of what is said outside of it.