There are partnered streamers that play copyrighted music on stream. As it is right now, the only thing that will happen is that your saved broadcast or VOD of your stream will be muted in parts where it detects copyright.
Your live stream will be fine and you won't get in trouble. If you need an example or proof, Gothalian is a popular twitch partner that has 5k viewers most of the time and he constantly has music going that is both popular and copyrighted.
I've also had friends having song requests for their viewers playing copyrighted music and they have gotten partner while doing so. So, no, I dont think you'll get in trouble or hurt your partner chances but if you're that worried, check out Monstercat as RepentGamingTV suggested.
Hope this helps