[Nyororin]

The plugs in Japan are the same shape as those in the US - minus the third prong (ground) in older buildings. In other words, neither of the plug shapes will even fit into a Japanese plug.

The voltage in Japan is 100V, so even with a direct adapter you may encounter problems. I would not recommend using the type of thing Polar suggested with something that is not compatible with 100V. I doubt it would damage it at all, as the voltage is lower, not higher, but it may not work so you`d be stuck with a useless item.

My best advice is to pick up an inexpensive one in Japan - you`re likely to have no trouble finding one that will be able to be used back home (with a cheap plug adapter) as Japan makes so many products for export.
Or, to pick up a voltage adapter. Be careful to find one that is approved for use with heavy electricity consuming items like hair dryers and straighteners. The cheap ones usually don`t and will short if you try to use anything like that.

In the end, the price of a cheap straightener in Japan is probably going to be similar to the price of a quality voltage adapter.