A c-stick of any A move (or shield roll) comes out the first frame possible, so it will be faster. You just have to train your hands to use the c-stick quickly. Not only that, but when you're using the control stick to uair, you might accidentally cause DI or even jump, which totally messes up the combo.
All I can say it practice the timing when you actually hit someone. If you hit someone with uair, there is a slight delay in L-cancelling before you hit the ground because of the hitlag. Practice on a heavy character and have them stand on a platform above you and just shffl uairs (stadium, dreamland, yoshi's). Plus, percentages play an important part in this. Find the right % (ex: for marth - at or just a bit over 0%, ganon - around 50%) for the character you want to combo and attempt your throw/nair/uair -> knee chain from there. Too high a % will make them fly out of reach, too low of a % and they'll just land early.