Well, it sounds like you may be able to solve both problems simultaneously.
If the mic is too senstive and you're having to tone down your vocal volume to accomodate, you may just want to dial down the gain. I've never used a USB mic before, but they don't seem to have gain knobs on the outside, so you probably need to adjust the gain via a driver. If the gain is cranked super high, not only would that explain the sensitivity, but also the excessive white (i.e. circuit) noise. You may not be able to eliminate all noticeable traces of white noise, given that the CAD Audio U37 is a $40 condenser, but if you haven't taken the time to fine-tune your gain settings yet, you should start there.