I think the “.local” extension stands for zeroconf devices. So you could just try to disable zeroconf.
On Debian: systemctl disable avahi-daemon
As mentioned below, disabling zeroconf is quite a no go, even if you use correct method for Wheezy. It will indeed avoid to reach PiMusicBox using its zeroconf name
If this listed share is Samba, use update-rc.d to remove Samba daemon: update-rc.d smbd remove
As I don’t use Airport I can’t help but @kingosticks replied here to shairport-sync password issue:
I’m not sure. Disabling zeroconf is rather drastic and since Pi Musicbox is still using Wheezy, that systemd command to disable avahi won’t work anyway. I would guess there is probably something in the samba config that controls the advertising.
All shairport-sync config is now defined in /etc/shairport-sync.conf and it includes somewhere to set a password.