What would they look like?
It's not about how they look (aside from the stupid 2-D "ripple of light" shock wave effect that
The Undiscovered Country pioneered), but about how spaceships in sci-fi are rocked by turbulence when an explosion goes off near them, because that's what we expect to happen from Earthly experience. Without a medium to propagate shock, the only hazards from a nearby explosion would be debris (if the object exploding isn't completely vaporized) and radiation. Although in one or two books I've rationalized the "blast turbulence" as the result of the radiative heating flash-vaporizing the surface layer of paint or coating on the hull, which would have an effect equivalent to a small explosion going off on the hull (because an explosion is the result of a solid instantly vaporizing and expanding with force).
Although it's true that explosions in vacuum would not look like the roiling fireballs so beloved in movies and TV, because that roiling is the result of fluid mixing as the gas and dust expand into the surrounding air. Without air to mix with, you'd just have a more or less spherical cloud of gas and debris expanding and dissipating swiftly, and of course without oxygen you'd have no fire. A nuclear or antimatter explosion would be a blinding instantaneous flash followed by a similar expanding sphere of vapor, though it might expand too quickly to be noticeable. Most of the prolonged blast effect of a nuke in atmosphere is a function of a large mass of the surrounding air being superheated to plasma and forcibly displacing the air around it as it expands, so without that air, the blast is brief and less intense, with radiation being the main hazard.
Most real explosions don't look like those roiling orange fireballs, which filmmakers prefer because they're fairly weak, low-energy blasts, meaning both that they're relatively safe to work with and that they burn through the reactants slowly enough to be visually impressive. High-energy explosions, the really dangerous ones, are such fast and powerful reactions that the fireball might last only a split-second before the reactants are consumed or blown far enough apart to stop reacting, so you'd get just a brief flash of light, a powerful spherical shock wave rippling the air and expanding at the speed of sound, and a massive cloud of smoke and dust. They'd often set off explosions like that on
Mythbusters, and they'd have to advance through the video frame-by-frame for the fireball to be visible in just one or two frames, and that's with a high-speed camera.
(Trek can always write it off by saying it's due to the properties of some chemical or device that doesn't exist outside of Trek, can't it?)
No, because again, most of the effects we associate with explosions, like fireballs and shock waves, are caused by or occur within the air
around the explosion, so they're independent of whatever reactants create it. A shock wave is essentially a very powerful sound wave, so there's no shock wave without an atmosphere. (There is a diffuse interstellar medium that does create turbulence and propagate shock waves from things like stellar eruptions and supernovae, but only on a very large scale, and it's way too thin to have any noticeable effect on the scale of a starship.)
