You didn't say how the handles are installed. I assume they're the type that have one screw holding them on. If you can't get the screw out any other way, you might have to drill a small hole through the screw head. You can get a replacement screw. Be careful not to damage the outer threads of the hole.
If the problem is that you can't get to the screw because the decorative cover won't come off the handle, you might have to damage the handle to pry the cover off. You can buy a new handle.