I apologize if this has been answered before: Any ideas on cost-effective and safe packaging and shipping for baseball caps? I know bulk orders can be shipped in long boxes. How about when it's only one cap?
I would not recommend this method if your cap is the flat bill type. It might get bent in shipping. In this case, I would go to your local box store and buy the smallest box that will fit the cap bill without bending. It shouldn't have to be too big; maybe 4X6X2 high. the non-bill portion of the cap can be scrunched together so you wouldn't actually have to buy a box the same dimensions as the cap itself.
I use the shoe-size boxes for USPS Priority Mail. They're a little big, but they're free. Of course, these only work if you use Priority Mail for your shipping, as I do.