Can I play Wages of Pain hidden on one battlefield to a unit that is trying to conquer on the other?

No, you cannot.

According to RiftJudge FAQ #9433 (which specifically addresses this interaction with Wages of Pain), while you can react by revealing a hidden card at a different battlefield than where the showdown is occurring, you are bound by a strict targeting restriction:

Hidden cards cannot target units at a different battlefield than where they are hidden.

How it works:

1. The Reaction: When your opponent moves a unit to a battlefield, it creates a showdown. This event allows you to play a reaction from anywhere on the board.
2. The Targeting Constraint: Because Wages of Pain requires you to "Deal 3 to a unit at a battlefield," you must choose a target at the same battlefield where the card is hidden (Rule 811.1.d.2).
3. The Result: If the opponent's unit is at a different battlefield than the one where you hid your Wages of Pain, you cannot target that unit with that specific hidden card.

This is my interpretation based on Rule 811.1.d.2 and the cited FAQ. No official FAQ exists for this specific interaction with Wages of Pain, but the targeting restriction for hidden cards is a core mechanic.