A lot of 'RP' happens in group or guild, out of public hearing. NPC 'RP' happens completely within the NPC tab. I see no issue with someone 'singing' to only those who want to hear it (since a lot of people leave the sound off anyways). I think voip would be sloppy, though.
My suggestion: Make your songs, record them, upload them where your friends and others can download them, then do a simple /me starts to sing 'Old boat on the Radiant'. Those who have the song DLed can start to play it in an external program (or if someone has some coding know how, play it directly in the PS client with a /play <song>). Shortcut the lyrics if you wish for those not 'in' on the song.
As long as the songs are meant to be IC, and not 'Stairway to Heaven', I approve. For now, this would have to be a completely playerside initiative.