Wiring Ammeter with Shunt Question, wiring size?

YOu need not use big wire Common telephone wire will do. Or 20ga stranded (even smaller) Those wires likely carry less than one amp.

If you are worried put a pair of 1 amp fuses in the leads at the shunt that way heaven forbid the shunt burn out and try to pass all the current through the meter pop goes the fuses.