I don't think I've ever seen a colored stock tie; it seems to me like white and off-white base colors are what are worn generally. I have one that is white with navy pinstriping and I've never had any issues, so a white with navy piping should be appropriate. I'm not sure if it is a rule or just the norm to wear white but I would suggest sticking to white as a base with neutral accent colors (navy, hunter green etc.) if you wish - no hot pink piping or something of the like. I would suggest steering away from anything that is not a white or off-white base color though (if they even make those?). I am not familiar with Australia's rules so I would suggest to make sure you double check the national rules on the dress attire before your show so you know for sure.
I'm not familiar with ratcatcher shirts, so I can't say yay or nay to those.