Do not make a problem where there is none, or you will be ridiculed
I am sorry but this...
They also don't want other spaceships to be able to send any signals to the computers and other devices used by the crew on the ship, at least no signals that didn't go through the "comm tower" that handles normal ship-to-ship or ship-to-planet communication and data transfer.
...is an almost nonsensical concern.
Getting communications to work is not an easy task, especially not in the digital age. For reasons too long to explain here, I will state the following as a given fact:
You cannot "send a signal" to a device unless it is explicitly listening for one
If we were to rip out the radio units of your phone (4G, WiFi, Bluetooth), there is no way in hell you can "send a signal" to that phone without being physically connected to it. Magic Hollywood Hacking has led us to believe that we can access any device anywhere just because we want to but reality / realistic fiction begs to differ. Your readers will laugh at you if you create an environment where intruders can access computers at a distance and at will if those computers do not have a wireless communication interface.
...even if Eve & Mallory cannot intrude on systems that are not actively listening for outside communications, you still have the comms tower, and you still have devices that are listening for internal communications.
This means you must have communications protocols that are specifically made to avoid unauthorised communication and to reject intrusions. Especially handshaking is required to set up a communications channel before you can start moving any data. But — again — the device must have been set to listen for the signals to begin with.
The comms tower is set to listen. There you need to have protocols that are made so that no handshaking is being performed until the incoming transmission has authenticated themselves. Otherwise Eve & Mallory could fool your ship to reveal its location by broadcasting transmissions in the blind and triggering a handshake attempt. This however is not a big issue and can easily be automated.
Eve & Mallory have managed to steal the authentication keys.
Same thing for internal devices: they must be set to not trust any old transmission, but only those that can be authenticated. Again: this is not much of an issue, even present day communication protocols are designed for this (although not always successfully).
Eve & Mallory have gotten their hands on such a device that was not set to lock itself or self-destruct.
Finally there is EMCON... emissions control. This is good old fashioned radio silence and behaviour procedures for that are in effect even today. And — again — these are not always successful.
You had the notion that internal communications should be made only over wired devices.
That is a good idea, and is used in real life
Personal anecdote: I did my military service in the Swedish Airforce. My task was to ready aircraft. When military aircraft are on the ground and being serviced in a war-like situation, it is procedure to hook them up to a land-line. In our case the connector was clipped to an eye in the concrete pad the aircraft was being serviced on. So when the plane started rolling, the connector with be yanked out by itself. That way the plane could be radio silent the entire time it was on the ground, no confidential orders would leak, and it would not even announce its presence through its emissions.
Apart from that there are several schemes to make artificial emissions disappear among the natural noise, for instance LPI radars. But out in space, any emission from a point source is likely to arouse suspicion.
Levels of EMCON
Just like submarines have different "rigging" when it comes to sound management — which can be anything from We Do Not Care If We Sound Like A Rock Festival, in various levels all the way down to Do Not Even Talk Loudly — your space ships most likely also have that. The EMCON can take many levels from Noisy (all comms operative, space radar/lidar, jamming) to Quiet (no active comms, low intercept mode) to Stealth (everything that can emit is shut down).
In order to enforce this, I would recon that all emitting devices on-board can be turned off down by a "shut up" command from the ship itself.
— Captain? I am picking up an unauthorised signal... from within the ship!
— Who the hell brought a friggin' PlayBox on board?! Kill it! Turn it off, turn it off now before the enemy... oooh crap...