[Not a lawyer], but even so I don't think copyright is the biggest potential issue.
You could go the whole hog and invent a character set (as Iain M. Banks did for the "Culture" series (http://omniglot.com/conscripts/marain.htm)), or represent the spelling with standard Roman characters. The important question is whether, and if so how, you're expecting your readers to be able to interpret the symbols.
And here's the pitfall - some readers will want to do that, and they're likely to feel cheated if they can't, or if the alien language is nothing more than a transposition into a commonly known character set. These will be the readers who have most invested themselves in your work, so are probably those you least want to lose or disappoint.
I wouldn't use WingDings. The exception to this is if the story's logic holds, and there is some reason the alien race adopted WingDings, or that they were the inspiration for the person on Earth who created that character set. Otherwise, it could end up looking like a bit of a shortcut.