Sword spec never procs an off-hand attack.

Does sword spec work with offhand?

Nope. It only affects the hand which has the weapon, for any specialization except dual-wield (which only really affects the offhand because the main hand has no damage penalty).

Does sword Specialization proc on offhand tbc?

To answer all of the questions, yes, if you have a Mace/Fist in your main-hand with a Sword in your off-hand, and points in Sword Specialization, then the sword has a chance to proc the Sword Spec.