There was no such thing as an "Irish bouzouki" until some Irish-music player picked up a bouzouki (which is, after all, a Greek instrument) and played it along with his Celtic sessionmates or bandmates or whatever.

Any stringed instrument can be tuned in different ways, of course. I'm sure you'll find folks who can offer more specific advice. While it's probably true that the bouzouki is often used strictly as a rhythm (chording) instrument in enembles where fiddles and whistles, etc., carry the melody, it is certainly capable of being used as a "lead" or solo instrument. Google "Beth Patterson" for an example of a very impressive performer who sings and plays a very impressive Celtic bouzouki as a soloist, and who has also booked plenty of time playing the same instrument as the context of an ensemble (the Poor Clares).

Just don't let anyone tell you that you can't use your new intrument because it's not "Irish." It's a bouzouki, which means it's just like the first "Irish bouzouki" ever put to use in a Celtic-music context.