There are a lot of dice rolled in a session of Art of Wuxia: rolls for initative, rolls to hit, rolls for damage, action checks, resistance checks... and oh wait... which of those was my initiative die?!
This initiative deck gives you another way to track turn order. Deal each player a number of cards equal to their INIT score. Let him use whichever is higher as his initiative score for that round. If you have more than one card, the others could be used for tie breakers.
There are even two optional cards you might enjoy using: