Going from 3x8 to 3x9 is a pretty marginal gain. And it's not necessarily plug and play neither. Front Derailleurs over Triple cranksets are fairly hard to dial in. I generally think of the FD, the chain rings, and the chain as one inseparable unit with a triple groupset. They are designed to go together. When you randomly change one of these it might not shift cleanly any more.
So back to your original question- if all you are after, is a shorter crankarm, then you should have just bought the same crankset as you currently have, but with shorter arms.