I like BCrider's idea with the CO2 idea. Without a flash hole it would be pretty safe to have the pan functional for appearances without risking someone actually loading it up. Use something like the Girandoni hammer system blended with a modern striker fired air gun. The hammer would fire the striker in the butt stock, similarly to, but not the same as the Girandoni.
http://3.bp.########.com/-EkQet-9TDUI/T2va3L2s4wI/AAAAAAAAAgY/XtkB3oXMOyM/s1600/pistol-pcp-hammer.jpg
Alternatively, a true BP flintlock could be made with a chambered breech like a small mortar (seeing as people do make golfball mortars I figure it would be appropriate), and relatively light walls. The patterns on the barrel could be tigged or silver soldered on as shaped cutouts. Your dimensions would probably have to change a little too - since it looks like they didn't leave enough room between the trigger plate and the bottom of the barrel for wood.... since it's a prop they didn't need to factor for such things like not having space for the back/bottom half of their barrel. I can see how it could be made to work with those dimensions, but man... you would not have a lot holding it together.
Aniest is probably on the best track by making it massive, (the one in the picture looks to be the length of the guy's fore-arm, or longer) even if it would royally suck to hold. I'm personally against sleeving a smaller barrel inside a bigger one, partially because it would be more fun to shoot a golf ball than a normal .50 round ball, and because you're going to end up with more weight trying to hide the inner barrel, long flash holes from the pan to the charge, difficulties in disassembling and cleaning etc etc. Once the ball size and weight has been determined, then you can go about figuring out what pressures you'll be dealing with. Most smooth bores (and shotguns) have surprisingly thin walls, and barrel thickness reduces even more approaching the muzzle. With a chambered breech and dedicated powder charges I suspect the gun wouldn't be outrageously heavy for its size.... but hard to say without doing the math.
Also as has been said, if you're paying anyone who is A) actually able to do it well, and B) is realistic on their budgeting, expect to pay several thousand or more. Skilled time is by no means cheap.