I could be very wrong, but here's the theory:

The game calculates dual wielding attack AP cost by doing this:
Weapon 1 AP cost + Weapon 2 AP cost - A fixed value (default is 2) = Attack AP cost

If you set AP cost of both weapons to 1, this becomes:
1 + 1 - 2 = 0 AP

Have you tried equipping the 1AP dagger on one hand, and a sword on the off hand?

If my theory is right, the attack cost would become 1AP.