False. Saying "Four" takes a negligible amount of effort and time. Saying "Score" takes a negligible amount of effort and time. Reciting the Gettysburg Address requires a lot of time.
Similarly, if you hold 100 marbles in your hand and drop them one at a time (free action) while counting up to 100 (free action), it does not take 200 Free Actions = Free Action. It most likely takes all of your actions for several minutes.
Very few free actions actually take _no_ time, most take a small enough amount of time they can be done while you do other actions.
Sorry, you are correct. "Free actions take almost no time or effort. You can take as many free actions as you want during your or another combatant's turn." (PHB pg 267)
I did leave the almost out of my post above. However, I still believe that this supports the idea that someone can swap hands as a free action.
At any time, the DM (or player) may decide that things take too much effort or time to perform as a free action.
Thats one of the benefits of being the DM, you get to decide pretty much anything at any time you like =)
But to support your statement, the above definition of Free action continues with, "The DM can restrict the number of free actions in a turn."
So, in other words swap hands it a free action.. unless you DM says otherwise, pretty much as normal.