I'm reasonably sure you can use the same brifters. I just changed from a 9 speed Ultegra triple to a Force compact double. I changed the FD, RD (short cage, optional), BB and chain.
The brifters have 4 clicks. In a triple configuration, you get a trim adjustment for the middle chainring only. On the compact setup, you have a trim on both rings.
BTW, I have all the triple components and will let them go for a fair price. PM if interested.