I don't know the character but I do know what flywire is, so I'm assuming the character you are doing has illuminated eye outlines? That's what this stuff does. If that's the case and look you are doing, I would skip trying to do the transformer and adapter and just use some EL WIRE. It does the same thing, you get a lot of length, and its wired into its own power supply with a toggle switch. It is also cheap, and runs off 2 AA batteries.
Here is a link on amazon (many colors).
http://www.amazon.com/s/ref=nb_sb_noss_1?url=search-alias=aps&field-keywords=el+wire
I used it in my Halo MK V and its pretty sweet, and bright. You can also cut any excess off if you don't need it, just cap the end with hot glue or electrical tape, or rubber.