It's not odd, but we only say 'male cousin' or 'female cousin' if we really have to. If it's essential to make clear that the cousin is male or female, then we do use these terms. In academic contexts, such as genetics papers, these terms would also be used. Otherwise, in everyday English, we'd just say 'cousin', in the same way as we'd use any other non-gender specific term, such 'friend' 'neighbour' 'teacher' 'boss' 'classmate' or 'colleague'. In all of these cases, it may not matter whether the listener knows if you're talking about a man or a woman, and if it does they'll probably pick up a clue from pronoun such as he/she/him/her at some point.