Sailing a bigger boat, keel boat or cat, is probably beyond what was intended for this Forum ....however, being one who believes that we never stop learning, I'll start by saying that chartering is hugely fun, a great adventure.
Chartering has turned into a major tourist 'industry', in wonderful places like the BVI's, the Grenadines, Tahiti, Split, Dubrovnik, Turkey, Greece, Australia and elsewhere.
You want to know what is needed to sail a cat on a charter.....you need to demonstrate that you have the experience and knowledge to sail one of their charter boats safely, and be comfortable in those waters and those conditions.
Why not ick up a couple of magazines, Sailing, Cruising World, Latitudes & Attitudes....
If you want to go 'formal', perhaps you might contact your local sailing club and see about getting 'certified', that is, White Sail I, II, III, then perhaps Bronze IV.... then do the American Power Squadron first course, 'Basic Seamanship'. You may want to do more, like 'Celestial Navigation', although with GPS these days.....
The best way to get experience for your sailing resume is to get together with clubs or folks who own a keelboat or a cat, and do sailing with them......
One of the better options is to join a FLOTILLA... maybe six boats, and one Flotilla skipper. You'll be like little ducklings behind the skipper's boat, and you'll learn. You already know most of the basics...let the skipper guide you as to that day's course and anchorage. The sailing you'll pick up in less than 15 minutes.
That's how we started: after learning to sail on little dinghies (Albacore and Laser), we sailed H16s, a Bristol 33 out of Hyannisport, then H18s, then a berth on a 52' Privilege sailing around Antigua for a week, sailed a Hobie 15 off the beach (this is a Hobie from Europe), then in Florida a Wave, then a 29'er, then sailed with Alan on his Tiger (the best), then a berth on a Lagoon 440 in the BVI's, then a Sunsail 384 in the BVI's....live and learn.
Try
http://www.sunsail.com, they know their stuff.
email me off line for more info... can't wait to go snorkeling at the Indians and drop in at Willie T's for a drink....