Hmm. Maybe something like this, from a 1963 Douglas ad about a possible Mars spaceship:
At this early point (if I'm Jefferies), I still don't know how far in the future Star Trek
is, but I've gotta figure the Valiant
is much closer to our time than it is to Kirk's. The only clue I get on the ship's appearance is a reference to "old impulse engines," yet clearly some kind of FTL drive is also involved if we're going to the edge of the galaxy. (That rules out the later, pre-warp drive DY-100 'submarine' look.) This isn't the hero ship, it's a one-off that'll only be in one scene, viewed from a distance (one of the bridge monitors?) and on low-res mid 60's TV sets. It's gotta be designed fast and it's gotta be cheap.
Since I've been gathering a ton of spaceship art from every available outlet to figure out the hero ship earlier in the year, I don't have to think too hard about it. Grab one off the shelf ("Projected designs by real spaceship companies" section), throw a primitive pair of my hero ship's engines on there somewhere, and off we go. (In the case of the image I linked to, attach the nacelles to the long stalk at the rear of the ship before the main 'rocket.') In keeping with Jefferies' philosophy, the engines are kept well clear of the crew and easy to jettison if need be. Plus it doesn't look like either a simple rocket or an airplane yet conveys size and power, as Roddenberry would want it.