I have to use the wire I have. But Big Z is right, they make tiny thin wires now, and even circuit tape that can handle the load of LEDs. I lit an Enterprise D 20 years ago with 6 in florescent tubes, and grain of wheat bulbs... The florescent tubes could be on for 5 1/2 min before the thin copper wire powering them started getting hot enough to melt the styrene ... The tubes were in the nacelles of course, even in 1/1400, the nacelle supports were solid styrene, that I had to cut out channels for the wires.
Telephone gauge wire is about all you need for what you are doing. Conductive Epoxy is a good way to make switches using paper. This can connect to pieces by sliding a greebled part, to turn the ship or portions on. You can run traces with Silver exposy, and do way with wire completely. I use this stuff fto fix circuit oards, where soleer would raise the trace. Most I.C.'s are attached with epoxy these days.
What kind of power supply will you use? What do you think about what to do Li-Po battery powered model with built-in charger? You have enough space to accommodate even a large smartphone battery. I can suggest tested components and draw a wiring diagram
Thanks for the offer Kolokonikov, I'm using a 7.5V 1000 mA transformer that I have attached a female USB to. Power to the model is them provided by a simple USB connection. The nice thing with this is that the low draw displays (Darth Vader's lightsaber, etc. ) can be run off a power bank/laptop. I've found that the more intensive models (my Enterprise E and now Voyager) need a bit more juice to light up nicely
On that point, current LED count for Voyager sits at 28, with the primary hull still to go