I had this same question once about a vintage partial bottle of Miss Dior with a broken sprayer. Someone here advised me to use a dremel with a small circular file attachment (whatever that is called) to grind down the metal collar that surrounds the sprayer (whatever that is called) so it can be removed. It's quite a thin piece of metal so it shouldn't take long. I still haven't done that because I don't have a dremel (though I want one), so my old Miss Dior bottle sits there forlorn until I figure out what else I can do. If you have a dremel or other drill and the right bit/attachment, you are in like Flynn.