I don't mean to discourage you but Globals are somewhat notoriously difficult to sharpen properly. I have it from several highly skilled sharpeners very experienced with Japanese knives that the steel Global uses generates very tenacious burrs that are difficult to remove. In this instance I'm inclined to agree- sending it out to an experienced pro would be your best bet. One of the best in America is Dave Martell @ JapaneseKnifeSharpening.com.
Short of that you can buy waterstones and learn to sharpen, buy an Edge Pro Apex or try a less sophisticated pull thru sharpener like the EdgeMaker Pro.
The first option will carry a steep learning curve but ultimately can be very flexible and rewarding. The Apex is an incredible tool and will get your Global considerably sharper than it was new. The last option is not really the best way to go with Japanese knives but will inexpensive, simply and reasonably effective.