I've seen various osu! YouTubers have a similar fashion to avoid getting copyright claimed by YouTube's ID system.
- Increase the hitsounds to make them louder than the actual music. If you're willing to go through the extra mile such as replacing the live version's audio, you can record the reply version with much louder hitsounds.
- As mentioned above, talking over the audio clip or raising or lowering the pitch is pretty effective still. This goes for replacing the audio with non-copyrighted music as well.
- On YouTube there used to be a feature where you were able to type in specific song names and it would have let you know if it was copyrighted or not. Sadly, as of today your only option would be to upload the video straight up and let the system hit you with copyright and then edit your livestream later.
- Possibly what you could do for future livestreams is have your own category on osu! that features non-copyrighted songs to avoid future copyright claims.
Hopefully in someway these ideas could help c: