You get the shinai by trading your wooden katana or lotus katana to the "???" mark that pops after the armor is defeated.If you trade it to a mithra's ??? it gives you a neck armor that has 10 charges to tele to that area's chocobo stables.
The best setup for this is RDM/RNG. Before you talk to Nomad Mog use Protect4, phalanx, haste, and stoneskin. You can almost solo a normal armor with this. Even the mithra armor cant touch you till phalanx wears. And Always CHANGE YOUR HOME POINT!!!! I dont care if you want to keep your Whitegate HP! Its just a boat ride away! Saves alot of time waiting for raise and weakness to wear.