Yes, You Can Use It
It doesn't say that you need a free hand to make this attack, nor does it say that you need to be holding a particular item in hand to make it. So you can use the maneuver even if you used Two Weapon Fighting in the last round. The fact that it's a touch attack is just to tell you what AC number to roll against.
It would be very hard to use if that wasn't the case, as things like shields, two handed weapons, and even a torch would interfere otherwise.
Although not a rule, the flavor text gives you a hint about how this works:
You focus the pain from a wound you have just suffered into a fiery
manifestation of revenge.
The maneuver in this case is actually fire shooting off of you when someone else hits you and hitting them back, so you can picture it working without you having to have an empty hand.
No Penalties For It Either
Using Two Weapon Fighting imposes a penalty on your attacks (-2 in your case), but those penalties don't apply to this attack. The reason why is this:
Once you take a two-weapon fighting penalty, the penalty applies to
all the attacks you make with that hand during your current action. It
does not apply to attacks you make during some other character's turn.
The reason why is that Two Weapon Fighting doesn't specify that its penalties last outside of your action. Compare to something like Power Attack, where the effects last until your next turn.
So, go ahead and use your twin daggers. It doesn't affect your use of this ability at all.