If an opponent plays Hidden Blade from hand, and I react with a Hidden Tidehunter, does it save my unit being targeted?

No, playing Tideturner from Hidden does not save your unit.

Hidden Blade played from the hand only requires its target to be "a unit at a battlefield" — it doesn't lock to a specific battlefield location. When Tideturner's play effect swaps the targeted unit to another battlefield, that unit is still at a battlefield, so it remains a legal target. Hidden Blade resolves, kills the unit at its new location, and its controller draws 2 (FAQ #7179, Rule 359.3.e.2).

This differs from Hidden Blade played from Hidden (facedown), which has the extra "must be at this specific battlefield" restriction — moving the target off that battlefield would cause it to mistarget (FAQ #210, Rule 811.1.d.2). But from hand, location doesn't matter as long as the unit is at some battlefield.