Unfortunately we're not in control of the shipping process for international entries, so we can offer only suggestions, rather than guaranteed advice, about how to ship your meads for the competition. Several folks in years past have had success shipping with private carriers, such as DHL. Others, depending on the country, have had no issues with shipping via their country's postal services. But in other cases (which appear to be related to the country of origin), meads have been intercepted and turned away at the border - regardless of the shipping method or the carrier.
Generally we advise prospective international home entrants to try to ship using the same instructions that we give to our domestic entrants - to package your meads securely, and to ship them in a non-descript container (such as an unmarked corrugated cardboard box). When you declare the box's contents, if you mark the box as containing alcoholic beverages - that can create problems at our receiving ports, since the existing customs law in the US requires that taxes and duty be assessed on all alcohol shipments entering the country. The laws were written to ensure collection of tax on commercially produced product destined for retail sale, but there are no explicit exceptions for non-commercial home products. So depending on the mood of the customs agent, your home shipment may be cleared, or may be stopped and either destroyed or sent back. We have found that people who declare the contents of their bottles to be something that doesn't suggest there's alcohol inside, have greater success with their shipments.