Yes, you can do this in OBS without using external speakers. Add a Media Source in OBS (click the plus icon in Sources, then select Media Source). Point it to a local music file or playlist. The audio from that source will go directly into your stream mix without playing through your room speakers. If you want to hear it yourself too, go to Advanced Audio Properties in OBS and set the Media Source to Monitor and Output. That way the music plays in your stream and in your headphones, but does not come through your room speakers and cause feedback.