Default security settings for offline content are quite strict; because offline content is supposed to have access to its immediate environment (the user's filesystem) For that reason, you may not be able to disable security dialogues. They wouldn't be very secure if you could.
If your hyperlinks are just hrefs to the files on the user's computer; you have absolutely no control over how a browser or a user chooses to deal with those files; in the same way as you have no control over whether a user chooses to open or save a file when presented with a download box. There's plenty of good reasons why.
If you were to change your tactics somewhat, and embed the music onto your pages; you'd have alot more control over the display of the embedded media player; but perhaps still security errors if you're accessing local content (files on the user's machine), and it'll be more work for you developing a way to access the (hidden) media players.
For code to embed a WindowsMediaPlayer into an HTML page:
http://www.mioplanet.com/rsc/embed_mediaplayer.htm
If you want to hide that player, remove this line:
style="position:absolute; left:0;top:0;"
and replace it with this line:
display="none"
if you want it tonot play automatically; remove this line:
<PARAM NAME="AutoStart" VALUE="True">
and see the bit at the bottom of that page for controlling the player using Javascript. [insert your media player ID].start() probably works to start a media player that doesn't have auto start enabled.