Sensors. They even have sensors to point out they're not in the same universe. In short, physically disguising a ship as something else, would work for exactly one second. In even shorter: the idea is nonsense.
Except of course not. Clever paint jobs and canvas smokestacks can fool the sensor called the eye. Our Starfleet heroes in TNG, DS9 and VGR frequently use other kinds of clever jobs to fool other kinds of sensors, typically at long ranges: the hero ship can be made to look like a harmless merchant or a vessel from the ranks of the enemy when it is observed with sensors that identify warp signatures or whatnot. It never is a perfect disguise, but disguises never need to be.
The trick supposedly would be to fool the enemy at all ranges. And while Sisko or Janeway could just erect a hologram to alter the looks of their ships, Lorca or Saru or whoever would not yet have that option: TAS showed them operating holograms indoors, but external holo-camouflage was still novel to them in "Sharper Than a Serpent's Tooth", say. Hence a ship that can semi-plausibly be given the smokestack job in addition to all the standard sensor-fooling trickery would nicely serve the needs of the job. Although of course it would dramatically go so that it's a happy coincidence that the hero ship can be made to look a bit like a certain enemy ship, rather than a hero ship having been built to look like an enemy one. (Real-world commerce raiders were seldom specifically designed for their job, even if they were heavily modified for it.)
Whether there's anything to the story offered in the original post is one matter. Whether it would have been fun to see the hero ship disguised, with a bit more than the painting over of a single letter, is another. It's something we basically never see, our heroes working on their ship's exterior. I for one would have loved to see that.
Timo Saloniemi