Can I use action spell cards on opponent such as Wages of Pain/Bellow's Breath even though I have no units (it's a non-combat showdown right)?

Yes. A Non-Combat Showdown still counts as a Showdown with an Open State, and you can play Action spells during it even with zero units on board.

The opponent's move to an empty battlefield you don't control applies Contested and stages a Non-Combat Showdown (Rule 344.2). In any Showdown, each player in turn — regardless of whether they have units there — gets Focus and may play Action/Reaction spells (Rules 345, 347; keyword Action per Rule 806.1.b). The mover gets Focus first, then it passes to you, so you'll get your window.

As for the cards: Wages of Pain targets "a unit at a battlefield," and Bellows Breath targets "up to three units at the same location" — the opponent's moved unit is a perfectly legal target. Your lack of units doesn't matter for either spell. Just keep in mind each spell closes the chain once played, so the opponent can only respond with Reactions (FAQ #7200, #2682).