Wedding locations do operate on holidays, and, in fact, will take advantage of such days in that most folks do not work, so getting married will bring a good number of folks to the place to, uh,...spend money.
Plans are often based on what we want to do, along with various things that should or have to be done in order to accomplish that sought out goal. There will logistical concerns, potential problem concerns, and there will always be our dear ole friend Murphey, throwing his law, as wrench, into the works.
We do not know many of the details, and so cannot really help out that much. As questioned above, her wife-to-be's quiting her job and going over to the States for a month, then coming back to Japan, strikes me as odd. (but you see, it could just be that I don't have some detailed information that give me any other vision of it)
I somehow do not see the connection between your wife-to-be's getting a green card and, as I put what little pieces of information given, together, you're desire to work here in Japan in the future. Unecessary paper work and trouble?