If you think you're looking at a missile in a sense you're not far from wrong.
I decided to try making my version of the Valiant
more elemental. That meant trying to stay away from anything a bit too elaborate for the era (in my opinion). If, as I conjecture, fast relativistic ships were being used prior to the introduction of Cochrane's space warp then they might try to adapt the new development to existing hardware. It certainly would save some time and money initially rather than going for something wholly new from scratch.
What might a fast relativistic ship look like? To get 80-90% light or a bit better your ship would most likely be something of a projectile shape and not too far removed from the V2 rocket shapes of '40s and '50s era sic-fi or perhaps something roughly similar to contemporary missiles, ICBMs and heavy lifting or satellite launching rockets. And note that the (by now) decades old DY-100 ships were also reminiscent of a projectile shape (with add-ons).
And so if we can assume Cochrane's new space warp technology can be adapted to existing 21st century designs then that can be a starting point to envision what one of the first generation of FTL ships might look like. Hence the image posted above of the main section of my version of the Valiant.
Areas that had previously been devoted to extra cargo and fuel some of that could now be modified to refit the new FTL technology to the ship. The main section overall could conceivably have gotten a bit smaller (or shorter).
This is still essentially the same as my previous design except that I've devolved it a bit to make it look more of TOS' mid 21st century era. It will still be more elaborate than the DY-100, but then it has to be while not being too far removed from it.