I don't know anything about prop sizes and Hatteras yachts in particular. That said, as stated it is more of a science these days and the prop shop makes a huge difference. I went through 4 of them before I found the holy grail of prop work. I have Acme and Veem and the Veems are a thing of beauty for sure. The diameter is limited by how close to the hull that the tips pass - closer equals more noise. The diameter is dictated by the engine loading so that WOT develops the correct RPM, say 2300. The number of blades is usually a tradeoff between faster (less blades) and smoother/quieter (more blades). You get rpm vs speed data and the WOT numbers for both sides and the distance to the hull and a quality shop/vendor can dial in what you need based on your goals. Not all manufacturers/prop series are equal. Some have cavitation problems for instance where a prop can be destroyed from the impact damage at the blade/hub interface. If you ever find a great prop shop that gets your wheels really dialed in, get them drilled for a propsmith or get a proper puller so that the yard doesn't beat the crap out of them and your transmission thrust bearings. Also make sure that they lap the tapers to the proper contact percentage as well.
George