I know that you think that a cord will drag your mouse around and decrease your accuracy, but you'll find that the cord is barely heavy enough to feel and definitely not heavy enough to impede mouse movement. Plus the lower latency is pretty essential if you ever plan on playing a hitscan class.
For your price range, i'd recommend a Logitech G400s, a very good mouse with very few issues and a decent RMA policy if any arise. It also has a near-perfect optical sensor and is one of the cheaper mice to do so.
As a side note, DPI doesn't mean shit other than simply raw sensitivity. It doesn't control really anything other than onscreen sensitivity. Good mice don't necessarily have higher or lower DPI, it's really just sensitivity and nothing more.