can't override nice menus css
I think you are making it sound more complicated than it actually is. (smile)  

As explained here, you may consider simply registering  your custom stylesheet in your theme's .info file:

stylesheets[all][] = nice-menu-custom.css.


Once that is done, you have the benefit that your custom style-sheet will be loaded with all other application's css and js files,  and be optimised by Drupal (when you change your dev settings to prod settings).

You understand that you can then overide any nice menu selector in your stylesheet, as long as your stylesheet loads last it should do the trick. If you want to "delete" an unwanted style, do not hack nice-menu.css, add an empty matching selector selector in your style-sheet.

THen, last but not least you can confirm your custom styles are being loaded by looking through any browser's inspector applet or script viewer, or even view source. Whatever.  In dev mode (no caching, no script compression) you should see the changes without needing to drush cc on your instance.

Hope this helps, good luck