Just having a look around resources on the 'net. It does seem that Hero players and GMs are quite prolific :)
I'm be going with traditional martial arts for the Western Shores. Other nations would have their own of course - the Feline empire to the east, being a fantastical version of medieval China, would have what is commonly thought of as "martial arts" (ie unarmed combat).
But for most folk it will be - http://surbrook.devermore.net/herosource/medievalma.html
Well, for military professionals that is. The common folk would have "farming arts" or "craftsman arts" :)