Don't worry unduly about that "Scotch" business, by the way. I used to be one of those who objected to its use for other-than-food items; until, that is, I made the small effort of looking at the history of usage. Turns out that "Scots", "Scottish" and "Scotch" were used interchangeably, and with no value judgements attached, by Scottish people as by everyone else, until well within living memory. The fine distinction made nowadays is a matter of fashion as much as anything else. People who make a fuss about it are usually -present company excepted, of course!- just ignorant (as I used to be on the subject) or trying to show off, or pick a fight.

Generally speaking, I'd think the term "Celtic" to be fairly unhelpful; again, it's largely a fashion-product, and not really much more indicative of a commonality of style or repertoire than "European" or "Asian". On the whole, I'd stick with "Irish", or "Scottish" (as appropriate), for instance; it gives a much better idea of what's meant.

You'll be relieved to find that I have nothing to add to what has already been said about the word ceilidh!