Ws2812b circuit safety with 5V 12A
My question is what gauge wire should I be using?

The recommended wire size for 13A is 19AWG (which is hard to find) so get 18AWG. 3.5m of 18AWG wire is about 0.12Ω, which would be about 1.5V of loss. So a larger size of cable or paralleling the wires (multiple strands of 18AWG) might be the best way to go.

Should you put a fuse in the circuit?

If you're worried about something shorting and heating up, then yes, put a fuse in. A 20A fuse would ensure that you don't blow the fuse but protect against short circuits.