Not that I'm aware of. Some miltary units have worn the khaki ones, some have worn green, but I think the light blue is a recent invention with no miltary/police connection.
I could swear I remember reading somewhere that Jacobites in the '45 wore light blue bonnets, but I could have been imagining that. Or maybe it was just a traditional Scottish Highlander color from the past. But I thought the sky blue color had a longer tradition and wasn't new?

Now, here's a question for you: are you used to wearing wool caps, commonly referred to as stocking caps, toques, or, (in the southeastern US) To-boggins? If so, then that's how warm a Balmoral will be, especially in the summer.
Well, I do have a knitted stocking cap that I only wear when working outside around the homestead in winter. Any time it's below 50 degrees, my ears get cold and I get a headache, so I pull it down over my ears. It's nice and toasty.

But since a Balmoral doesn't cover my ears and doesn't sit any lower than the brim of any other hat, I don't think I'm too worried about it being overly hot in summer. After all, if you can wear a heavy 10X beaver felt black cowboy hat in the summer sun when it's 110 degrees outside, a wool Balmoral probably won't be much different.

I just bought a Balmoral, dark green, from Celtic Croft...still awaiting its arrival. It should look good with my Isle of Skye kilt.
Yeah, I looked at their site and I like their price. But they just didn't have much selection in colors.

When you get it, I always advise soaking it in cold water, shaping it, and letting it dry. That'll take the crispmess out and make it look "worn." You want it ffloppy. Be usre to put it on your own head while wet so that it conforms to your head.
Good advice, thanks. On wetting it, should I soak it completely (like dunk it in a sink full of water) and squeeze the water out first? Or is there some other level of wetness or some other method for doing this that you'd recommend?