When I sold a wii fit, I had a big box and just cut it to try and match the dimensions of the wii fit box. A lot of tape was needed to hold it together, but it arrived safely at it's destination.
I would check the post office to see what kind of boxes they have. I would go my route if it is the last resort.
I shipped it through USPS for priority mail.
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You can also go to USPS.com and look at the boxes. They should have boxes on their site that you can order and you can see the dimensions it list them as. I believe the flat rate boxes should be free.