I was not able to dual wield rapier and dagger, I was pretty sure I should have been able to. 2 short swords was fine, short sword and dagger was fine. As soon as I equipped the rapier, no more dual wield.
This is because while a Rapier is definitely a 'Finesse" weapon, it's not a "light" weapon.
As an aside, having had a chance to hold a rapier myself, I can attest to it not being light in the slightest.
