If you aren't making money or trying to make money off of your youtube video, then the likelihood that a music publisher will actually bring a lawsuit against you for playing a song they own is almost zero. The worst that will happen is that youtube on behalf of the music publisher will ask you to take down the song, but that's it. There is a misconception about what happened in that lawsuit between Prince's music publisher and the family. The family is actually the one that brought a civiil suit against the publisher, alleging that they were abusing the Digital Millennium Copyright Act by bringing an infringement takedown notice against the family, which was not a lawsuit, but only a takedown notice. Music publishers are mostly concerned about people who are allowing other users to download or replay masters (the original songs). As you can see from the myriad of covers out there, it's more the exception, rather than the rule, that covers lead to takedown notices, and even then, they are unlikely to lead to lawsuits. This analysis changes, however, if you're trying to make money off of your cover somehow, e.g. by selling ads or selling mp3s of your performance.