You definitely can. The combination of white chocolate and crushed peppermint candy is a no-fail, which is why it is highly recommended. However, you can still use any other kind of chocolate if you’re not a fan of the sweet white chocolate has.  Dark chocolate or milk chocolate both work really well too, and if you want to bring some extra fanciness into the picture, you can have a layer of milk or dark chocolate, followed by a layer of white chocolate and then the crushed candy canes.  If you’re not using chocolate bars, you could also make do with chocolate chips instead.