Two ways I know of that may help.
You could you a media/music player on your own computer. Or if you are using Twitch to stream online with you can use Nightbot - it has a music player option.
However note: with either of those options, if you play copyrighted music you stream could get muted later on/after it's completed. Twitch itself will just mute the stream (now while you are hosting/live - but afterwards) and not sure how YouTube handles that stuff.
I'm sure there might be other ways, but those are the first two that come to mind.