Many players fear playing unorthodox styles because they both aren't used to and don't know how to play them. Often they spend so much of their mental energy trying to figure out what they should do that they don't consider it from the opponent's point of view. Doing so is a shortcut to finding out what you should do.
Here's an example. Suppose you are playing someone with a wristy forehand loop. It's spinny, and the amount of spin and direction are difficult to read. Every time he uses it you have trouble with it. You try to find tactics to avoid letting him use that shot, but this puts you at a disadvantage - you are adjusting your tactics to avoid your opponent's unorthodox shot, which, by definition, should be a weakness - otherwise it would be the norm, an orthodox shot!
So you look at it from the opponent's point of view, and realize that all that wristiness in the shot may give lots of spin and deception, but there's a reason most don't do the shot that way - it's hard to control! Perhaps not against a slow-moving shot, but against a fast incoming one. And then a flashbulb goes off in your head as you realize that your opponent can't really do this shot consistently or effectively if you attack that side, or just play quick shots there, or even serve fast. And so that's what you do!
Similarly, whenever you play an unorthodox player, look at it from his point of view. Does he have long pips that give back all your spin? From his point of view, that means he wants you to give him spin to return, but he can't do that with a no-spin ball - so that's what you give him. And so on with all other unorthodox styles. Always remember that if a style is unorthodox, there's a reason for that, and if you look at it from the unorthodox player's point of view, you'll likely find what exactly he doesn't want you to do.