Had my (administrative, not courthouse) oath this past Wednesday, there were men in 'casual suits' so no ties, and others wore a jacket over a collared shirt with nice jeans or non-matching trousers. No one was dressed super formally, and there was not much in the way of traditional dress iirc. There were some ladies in modest Islamic attire, and I want to say there was a woman in a shalwar kameez behind me but I don't remember super well.
If you want to wear your kilt, absolutely wear it. You might be the best dressed of your group but you certainly won't be inappropriately dressed. If your oath is as a courthouse I guess there's a possibility it might lean more smartly dressed overall but a kilt would still be appropriate!