I've heard some scary things about Nassau so want to be sure we're being safe if we don't go with the official cruise excursion.
Nassau is to Atlantis what Downtown Orlando is to Disney: Something you go through to get to the real attractions. Ever look at the crime stories in the Orlando Sentinel?
Nassau has a crime problem, but it pretty much limited to the parts of town tourists don't visit...much like NY, DC, LA, and on and on. There have been a few highly publicized crimes on tourists in the past several years, but you could probably count them on one hand. I've been visiting Atlantis for the past 10 or so years, and I am comfortable returning there with my young children.
That being said, I don't spend any time in downtown Nassau (near the cruise port) because it really doesn't offer anything particularly special. The good stuff in the Bahamas is at the resorts or on the water excursions.
Taking a taxi from the port on your own should be perfectly safe. There's a
regulated zone system in Nassau, so drivers are pretty honest. The only scam I've ever heard of is people who don't know about this system agree to prices higher than these rates, thinking they're out-negotiating the driver. If you don't negotiate, the fee is set. I always take taxis from the airport to Atlantis for my vacations, and the drivers are the nicest taxi driver I regularly encounter anywhere.
Also, is it awkward checking in and then checking out at the CS? I would think they would frown upon just using them for the wristbands, but I'm definitely interested in saving the $$$!
This is a very common thing and is not frowned upon. The Comfort Suites implements 2 night minimum bookings when it doesn't want people doing this.