There are specific visas for athletes that allow them to bring in regulation meeting sporting equipment.
Getting a firearm across country borders is not as hard as people think as long as you research the requirements of the countries you transit plus the airlines beforehand.
Some countries will have conflicting laws though.
From memory importing a firearm out of the UK requires the case to be stickered as contains a firearm where as US laws are the case mustn’t show it contains firearms. (My info on this may be out of date)