Fiction Research Request: Will wired networks always be more secure than wireless and creating a private internet

Thanks for any insights.

This story takes place in 2065 and the two characters (minor criminals) are members of a guild. They need to converse securely, and to do so, they enter a dream-like state that's something like technologically assisted lucid dreaming with networking. So, to be clear, they aren't in the same room when they do this.

My question is, how feasible would it be (as near as you can guess given this is decades into the future) for this guild to basically create its own private Internet so that they don't have to use "the Internet" to send secret communications? A sort of darkweb that others cannot access but that is supported by an infrastructure of physical cables within the city? I'm assuming they would not want to use wireless communications.

Or, if they had their own satellite in orbit, might that then make it safe for them to do this wirelessly? (keeping in mind that anything can be hacked with enough will and time...I'm assuming).

Quantum computing exists in this world, which I imagine makes a difference, but I'm no expert.