No power gains, just faster revving. Easier to bog off the line though.
Shift speed isn't much of an issue, it's more a function of your dashpot (return to idle curve) when you lift. My stock Toyota 4 banger with a steel flywheel drops to idle in less than a second in almost a straight vertical drop when you press in the clutch. The Cobra with the lighter aluminum flywheel floats down gracefully and gradually with a progressively slower curve.
The engine accelerates quicker when power is applied due to less inertia, and it can also decelerate quicker when power is removed. "An object in motion stays in motion...", yada, yada. Key is "when power is applied/removed", an aluminum flywheel won't cause faster idle drop and penalize slow shifting unless the engine is accelerating/decelerating. In other words RPM falloff has nothing to do with the flywheel weight but your idle return programming, which if stock, is more than likely determined by the original transmission gear ratio spacing. ie: a car that came with a close ratio gear box is going to be programmed from the factory with a slower idle drop, car with wider spread gears is going to have a faster idle drop; point is to have the RPM falloff on throttle lift to line up right with an average upshift. Nothing a retune can't adjust to your liking.
Cobra already comes stock with an aluminum flywheel so no real benefit; I replaced it with Fidanza with a replaceable friction ring because some of the rivets broke on the non serviceable stocker, and for the same reason you're considering it: to do it all in one go. And I got a packaged deal on a matched and balanced assembly.
If a flywheel causes knocking sounds, you installed it wrong.
If you're really picky and want to do it right, take your new clutch and flywheel to a machine shop with a $50; the flywheel should be balanced with the clutch you are using. Aluminum will be more susceptible to vibrations if something is slightly off balance and you'll feel it in the pedal and the shifter (if it's a direct linkage).