Figure out the weight of your cigars, humidification device (if any), packing and check the
USPS international priority and see if would be cheaper to use your own box or to move up to the medium flat rate box. If getting to an accurate scale is a problem, just guestimate: IIRC, cigars weigh on the average 1/2 to 1oz each depending on the size. A 12"x12" sheet of bubble wrap is about 1/2 oz.
In most, if not all cases, the USPS will beat the price of any of the private carriers (FedEX, DHL, UPS) by a significant margin.