**The Pokemon hit with Colour Change would stay their own type.**

> When a Pokémon with this Ability is hit by a damage-dealing move, Colour Change will change the Pokémon's own type to the type of the move that it was hit by.

**[Source](https://bulbapedia.bulbagarden.net/wiki/Color_Change_(Ability))**

Though Skill Swap is a Psychic type move, it doesn't change the target's type to Psychic because:

- Skill Swap is **not** a damage-dealing move.
- Colour change activates **after** it has been given to a Pokemon. So you'll need to hit a Pokemon with a damage dealing move to change its type after you use Skill Swap.

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**[Replay for proof](https://replay.pokemonshowdown.com/gen8customgame-1471646213-4b0j8xnkz8zh240hfhyz77yykewf35kpw)**

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So the Skill Swap + Ghost type move strategy won't work sadly.

However

> The strategy was probably because ghost is super effective on ghost, so after you skill swap them you can keep on using shadow claw and it will be super effective.
commented 1 day ago by Cicada

The strategy would work this way, but you'll need to hit the opponent at least once to give them the Ghost type. This would also work with a Dragon type move.

Hope this helps! :)