Wasn't really sure how to frame this in the title, but basically what I wanna know is, are character skin mods allowed? (I am aware stuff that changes the gameplay or would impact the run itself is not allowed).

That's entirely dependent on the game's moderators to decide. Some games like Portal allow it and it has become a regular thing, while others disallow it or haven't even thought about it. Make a post in the game's forum or ask in the Discord.