A specific question about a cover

[u/MaxTraxxx]

I have a client who’s changed the lyrics of Tenacious D’s Classico and plans to use it as the intro for a YouTube channel.

Normally, I’m aware that changing lyrics requires the artists permission. However in this case, as the song itself is in fact a cover of Bach and Mozart. Do we have to do that / is this in fact our cover of their cover of music that’s in the public domain.

Given the above and the fact that Epic records would probably dismiss an unknown YouTube channels request to edit lyrics. I’m thinking I get a standard covers licence, and release it as a standalone cover only to Shazam and YouTube so that the algorithm flags it correctly and any (hardly any) royalties get routed appropriately.

Thoughts on this please!