I plan to name my commercial web project as ____Snap. My website will be unrelated to what SnapChat is offering and in a different industry, but idea of short living content is the same.
The answer to the question "can so-and-so sue me?" is almost always "yes", regardless of context. Such a suit might be baseless, and it might get settled in your favor, but you still have to spend the time and money to defend yourself. This can be disastrous for a start-up that's trying to get off the ground, and it's how patent trolls make their money. (I'm not accusing SnapChat of engaging in such tactics as a rule, of course; I'm just pointing out that the legal system does allow for them.)
Whether or not you are likely to be sued is a separate question, and one that can really only be effectively addressed by a trademark attorney with full knowledge of the particularities of your situation.