Just to add
I found this thread when I did a search for "curly haircut glasgow," so I'm bumping it up for others like myself.
Also, wanted to second the recommendations for James Dun on Hanover Street. Got a haircut there last night and my hair is fantastic. I love it. He knows how to make curly hair modern and flattering and will pay attention to your actual kind of curls. Plus it's all luxurious at the salon--I got a free manicure while I waited!
I've heard good things about Elaine from Alan Edwards, but I went to the Giffnock branch of Alan Edwards and got a terrible haircut from someone who was supposedly a "curl specialist." So if you go to Alan Edwards, stick to Elaine.
But really, go to James Dun. I think you're in good hands with any stylist, and I would definitely recommend Colin.