That's what I'd do. Make a swatch, check gauge before and after, knit to the "after" gauge. I always measure the "before" so I have an idea how MUCH it's gonna shrink. But make sure it's a good sized swatch -- at least 4x4", but even bigger would be better. Because if it shrinks at the rate of about an inch per foot, and you only have 2" to begin with, you might not even be able to see the difference. With a hat that's probably not a huge deal I guess, but for something larger the cumulative shrinkage could turn out to be problematic.
You might still want to pre-shrink it, just so it fits to begin with.
The good news is that if a hat's a tiny bit small it's not usually a problem. Just makes it stay on better.