However my airport express is connected to my wireless modem via an ethernet cable. Is there a way that I can get rid of this connection and it all still work?
It has to be serving up IP addresses for it to work. Are you connecting wirelessly or over the wired network? Better question, why are you disconnecting it from the Internet? Are you not using it for internet access?
I've set up AirTunes without any internet connection ever. Strange that it doesn't work without it. Can anyone with deeper knowledge of that matter help?