Mmm...Okay, so this could be an offensive thing to say, but I'm not sure if the Irish and the Scottish qualify as Celtic together or if Celtic is specifically Irish -_-.
Having said that, in my prospective tale "Tuatha De Danaan" (named for the race of Celtic gods), the antagonists are the Fomorians/Fomorii. They are shapeshifting elemental beings with godlike power over nature. They'd make great fodder for a campaign if you're permitted to use them, as I don't imagine that any one should be similar to any others.
You should also be able to use The Fair Folk, right? Horrifying fairies may seem like a cliche, but honestly, the only well-known example I can think of occurs in Hellboy II, which isn't a very popular film. You could probably get away with reinterpreting a number of demons or dark gods as Fair Folk. Mix them with elements from Scottish folklore to make them fit if you must.
As a storyteller, I feel that it's not the most important thing that the source you draw from fits the story you're telling. It's more important to be able to make the source you draw from fit the story you're telling. In your situation, I'd not be above reimagining King Arthur as a haughty lord who bit off more than he could chew and had to turn to Scottish powers to give his blade the power to carry him to a higher throne. As long as it creates a solid base for the players to have some fun and expand the lore through their play, it can't be wrong, can it?