I think you don't have to charge it in the cradle. The power adapter will most likely plug into the cradle, but also directly into the 3DS. That's how it works for my cell phone.
A 16 hour flight surely is long, but if you can get 5 hours out of your 3DS that should be enough. (The first and last 30 minutes you can't do anything, then you have to factor in about 3 hours for lunch, diner, breakfast, toilet breaks, etc. Sleep 3 or 4 hours and watch a movie for 2 hours and we're at about 11 hours. The rest 5 hours you can play 3DS. Isn't that a nice plan? ;P And if you're worried you can always bring a 3DS AND a DS lite. Depending on the airline you might also be able to charge your handhelds inside the plane.)
I also took my DS on my flight to Japan (about 20 hours via U.A.E.), but didn't have a chance to play. :) There were too many movies available.
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