Umm, I believe to get there you will have to go out the exit next to the mail station place in the mountain. Once outside, you'll see this Rito that, if I'm correct, will mention something about the Flight Platform.
You'll need the Deku Leaf, the Wind Waker (obviously), and the magic upgrade or bottles with green potion.
Once the Rito flies off, you'll see these pillars of sorts. You will need to fly to each one with the Deku Leaf. Each pillar has a sign on it, telling you where the next one is. Use the Wind Waker to correct the direction of the wind. Once you're done flying to each pillar, you will come to this cave thing and inside is an Orange Rupee, and the box you mentioned. The box just serves as a means to get out, since you have a limited time to swim. Just push it to get out of the cave.