Hi there - I have responded to your post requesting photos, and thought I should respond here too. Seeing as Dame Shirley Bassey lived in Splott for a while, it's certainly a possibility that she sang at the Grosvenor. There's a way you can find out!
It may be worth sending a message to developer of her website,
http://www.dameshirleybassey.com, and seeing if the question could be put directly to her.
As for stories about the Grosvenor, I found an interesting link on the BBC website, which also highlights the building's impending demolition.
https://www.bbc.co.uk/wales/southeast/sites/streetsofcardiff/pages/stories_splott.shtmlCheers,
Matthew