You should provide a link to the product so that we can have a look at it. A datasheet would be great. I couldn't find the product you mention on the RS website. Not that it makes much difference, when I looked at a different buzzer the product summary just says 6-16V, 65mA, 3200Hz. That's it. "Tech specs", where you should find more information, has literally nothing, unless you find "supported languages: English" useful. Don't use RadioShack as a supplier if you're serious about electronics. DigiKey for instance offers very good selection tools, and has datasheets for all of its products.
Like Olin says specs have their reason. If the product would work at 18V and produce a louder sound, they wouldn't hide this from you, on the contrary, trust me.
Since it's an active buzzer it has an oscillator inside. Manufacturers usually don't tell you anything about that, I've never seen a schematic of a buzzer's internals. The only thing you can guess is that it will use a couple of cheap components, an oscillator for a piezo is a simple.
I found these schematics in a Murata catalog, where they show them as examples of externally driven circuits. Doesn't mean that they did it this way, though it's possible.
The left circuit uses a couple of discrete transistors, and if you ignore the piezo for a moment this may well work at 18V. Small signal transistors are often rated at minimum 30V. The question is: what will the piezo do at this voltage? I imagine the piezoelectric ceramic mounted on the brass diaphragm may crack.
The right circuit uses a logic IC, probably a CD4000 series. Those are often specified for up to 18V recommended operating conditions, so that may work as well, but again the piezo may be the problem.
Don't do it. It the datasheet says up to 12V then expect problems if you don't follow that.