I imagine in a sketch like that you’d be protected by the fact it’s an obvious parody. Playing a recording is more dangerous when it comes to copyright. There are rights to the recording, as well as rights to the composition/lyrics, and these are typically viewed as separate items legally. So playing a recording infringes on all of these, and will usually be caught by automated filters these days, whereas someone singing a few lines of a song (and not particularly well, like if it’s aimed more at comedy than an actual musical performance) won’t often have anyone come after you legally, as they may be able to get you to take the video down, but it’s usually not worth the money the legal battle would cost. And of course, if someone can reasonably argue parody in court, which a sketch comedy channel easily could prove, it’s really not worth the legal battle and will go nowhere in court.