It's not beyond contemporary technology to create a series of shells that collect, convert and direct 'emissions' to a given point wherein they can be released into a high energy environment (the exhaust) that effectively neuters any attempt to listen in on emissions.
Such systems don't need to be passive, electrically active and reactive phases could be charged to switch an entire material layer to shed/gather in a sequence that would void any attempt to pass useful information through the hull. Such an arrangement would likely be expensive in any non techno-magical era, but then, in an era of routine spaceflight every polity can be 'genocided' with ridiculous ease if their spaceborne protectors are compromised, so one imagines quite an effort would be made to ensure they aren't.
The designers would know perfectly well what ranges they couldn't shield against/contain and take account of that in any decisions re: what format/wattage onboard devices might take.
Moreover building a warship intended for space operations without equipping it with sensors capable detecting all bands of emissions in all directions would have to go down as a bad idea. Algorithms attached to the sensors can be used to detect any attempts to garner information on the internal workings by 'radar' returns and create 'noise' to match the return frequencies.
This is assuming of course the ships are operating in the light of day and not attempting more general stealth.
General stealth would be a matter of materials tolerances, absorbing man-made wavelengths whilst emitting natural ones shouldn't be too hard a design challenge with technology that routinely sends people flying about space though.
Have you thought about how your missiles are guided btw? I imagine in the 2xth century it would be trivial to blind missiles and even ship sensors before missile launch, that is, they have to have an idea of where their target is. The speeds ships and projectiles would have to be moving to outmaneuever simple tracking mechanisms on wide band emitters designed to overwhelm enemy sensors would need to be post-star trek, i'd think. 'Stealth-by-blinding'