If I move into a battlefield that's open, will I be designated as an attacking unit for the spell that can stun an attacking unit?

No. Moving into an open battlefield doesn't give your unit the attacker designation — that move creates a Non-Combat Showdown, not Combat, and attacker/defender designations only exist during Combat (Rule 437; FAQ #5513). So spells like Existential Dread ("Stun an attacking enemy unit") or Shadow's ability couldn't target your unit at that point.

The one caveat: if your opponent plays a unit via Ambush as a Reaction to that Showdown, the Showdown becomes a Combat Showdown and you become the Attacker (you applied Contested). From then on, your unit is an attacking unit and those stun effects can hit it.