Yes

You can ready a free, move, or standard action. That action can be to cast a spell that has one of those casting times. If that spell is also a ranged attack (which can be a ranged touch attack, a type of ranged attack), you can meet the requirements of the feat Deadeye Shot (PH2 78).

The DM may require the trigger for your ready action to be very specific, however, forcing the caster to predetermine target, spell, and maybe even target's square, depending on how strictly he interprets the ready action.

The DM may balk at such a task because the feat Deadeye Shot seems to assume a ranged weapon instead of a spell, but nothing in the feat's text mandates that. A manticore could use the feat with its tail spikes just fine, for instance.

If the DM continues to resist, point him to the Weaponlike Spells section of Complete Arcane, which says, in part, that

Any spell that requires an attack roll and deals damage functions as a weapon in certain respects, whether the spell deals normal hit point damage, nonlethal damage, ability damage, or energy drain. Such spells can threaten critical hits, can be used in sneak attacks, and can be used with favored enemy damage bonuses. You can even use a number of combat-enhancing feats to... improve the effectiveness of weaponlike spells... (85)

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.