(written from a Production point of view)
Conceived well into the CGI era, when it had become more cost effective, the Dauntless-class vessel was never envisioned to be executed as a physical studio model, but rather as a CGI build. "There wasn't time to build a physical model. Also, the Dauntless needs to distort when it goes into the slipstream, and that's really hard to do with a model.", Ronald B. Moore further elaborated. (Star Trek: Action!, p. 81)
The description of the Dauntless in the script which read, "It shows a STARSHIP, glowing with power, hanging in space. It's sleek, bullet-shaped, as though built for speed. And it's roughly half the size of Voyager"  was the starting point for Rick Sternbach to design the studio model of the Dauntless class. He later recalled, "The U.S.S. Dauntless, NX-01-A, was another one of those tempting bits of get-home technology that turned out to be too good to be true for the Voyager crew. Actually an alien ship disguised by the crafty Arturis (whose name is almost, but not quite, entirely unlike the name of the star Arcturus), the Dauntless was to be used against the humans as revenge for not wiping out the Borg when they had the chance, setting Arturis' people free. The phony Dauntless employed a variation on the different super-duper drives that had been tried but were not repeatable due to micro-plot fractures, thus ensuring that Voyager would take seven seasons to get back to Sector 001. The design of the Dauntless was described as being advanced, but still recognizable as Starfleet, hence the hull plating and thrusters and nacelles and so on. The basic division of shapes was the same, forward hull, engineering hull-type extension, and the nacelles, though the new "addition" was that of the slipstream drive emitter underneath. Remember the USS Relativity? No similarity whatsoever. Probably because of the art tasks required by other episodes, I didn't go much beyond the line drawings seen here. It wasn't a terribly complicated design, though the blended quality of the hull might have presented some unique CG model challenges back then, and I'll let Brandon speak to that." 
In late February 1998, Sternbach submitted a sheet with preliminary hull shape designs for approval to supervising producer for the episode VOY: "Hope and Fear", Peter Lauritson, which was returned to him on 4 March with a design chosen and with the request to eliminate a bridge module. "This is a tentative approval for this design. As I look at this, I wonder what it is about this particular drawing that the producers liked enough to circle it. I know they want the bridge module shaved off the top, so I'll smooth that over. But the first thing that I have to do is rough out a cross-sectional view for [Scenic Artist] Wendy Drapanas so she can create some backlit graphic designs. I'll rough in some interesting hardware shapes and get this to Wendy in twenty minutes or less," Sternbach commented at the time. (Star Trek: Action!, p. 43). Drapanas went on to create the master systems display featured in engineering.
The following day, Sternbach completed a set of two sheets with orthographic views. "I've been given orders to proceed with the top, view, bottom view, side view, and for and aft views of the Dauntless. I notice that I stepped the bridge in a couple of places. And there's little thruster and impulse vents, and some little chevron shapes on the nacelles. I'll reproduce all of the very vague details in a much cleaner form so it can be used by the the computer graphic people", Sternbach continued. (Star Trek: Action!, p. 46) The blueprints were submitted to effects supervisors Ronald B. Moore and Dan Curry for final approval. Sternbach later added, "The surface details were Starfleet, so those were well known. I suggested to Ron Moore (Ron B. Moore, that is) that we go with a warmer tone to the "new" hull, like a coppery color, to distinguish it from the cooler Voyager surface. And so it came to be." 
Sternbach's final design sketches were later sold on 8 August 2010 as Lot #398 in the Propworx "Star Trek Prop and Costume Auction", estimated at US$100-$200, where they sold for US$120 (including buyer's premium), whereas a set of seven sheets of preliminary design sketches was sold on eBay for $111.50 on 8 May 2011. 
After final approval the orthographic views were sent to Foundation Imaging, where computer graphic imaging director Adam "Mojo" Lebowitz was tasked to translate the design into a CGI model, closely supervised by Moore. "The sketches really only show us one angle of the ship, so I told Mojo to generate a 3-D computer model with some sort of skin on it. I don't care what kind of skin, but I want to see what the ship looks like rotating around", Moore elaborated. After remarking that in this stage a detailed wire-frame model was not yet necessary, Lebowitz added, "My first step is to create a rough outline of the ship. Building a computer-generated model is the same as building a physical model kit. If you start with a big block of wood, you start shaving off pieces until you've got a shape you're happy with. I used a cube and basically modified the shape, shaving pieces off or stretching it out until I had the shape Ron was happy with. Of course, using the computer is better than assembling a physical kit, because I can use the "undo button"." (Star Trek: Action!, pp. 45, 47)
Once the basic shape was decided upon, Lebowitz had Brandon MacDougall build a detailed wire-frame model in the LightWave 3D software as starting point for finalizing the model. "After we finished building the computer model, it had to be painted and detailed, just like a physical model. You add details to it, airbrush it, put windows in and add lights to it, and big engines that glow", Lebowitz elaborated, explaining the rendering stage of the build. (Star Trek: Action!, p. 79)
A particular difficult decision was the color of the hull. "We don't know the texture yet," Moore said at the time, "and we probably won't have an approved color until sometime in May. We have narrowed our choices down to five, copper dark, copper gloss, copper light, gray gloss and gray. The gray gloss is the most traditional, but I feel that the ship should be a bit more radical. After all, it may look like a very, very modern Starfleet vessel, but it's actual alien technology. Copper light is the one I like", Moore concluded, taking the cue Sternbach provided him with a couple of days earlier. (Star Trek: Action!, p. 77) The final color that was chosen was a gray with a copper hue.
Moore proved to be right in his assessment of the time it would take to have the model approved. Whereas Sternbach needed four days to design the Dauntless class, Foundation, from start to finish, needed seven weeks to arrive at a final version of the model.