Programatically altering a field formatter in Views
If you wish to display a field in a different way, there are a different ways to go about it.


Create a field template in your theme and change there. Just copying the field.tpl.php file would work changing the way the field is rendered on a node page. Note that field.tpl.php is a generic template which would be called on each field. You might want to try the specific template names like : field--article.tpl.php would get applied to all fields on article content type; field--body.tpl.php would get applied to body field on any content type; and field--body--article.tpl.php would only get applied to body field on the article content type.
Overriding the theme_field() function. E.g. Implementing the following functions in your theme's template.php file would do the same as with template copying THEMENAME_field__body__article(), THEMENAME_field__article(), THEMENAME_field__body(),
THEMENAME_field().
If the field is rendered in a view you could override it with the view template. To find out the specific template which you would need to override, click on "Theme: information" under the "Advanced" settings in the view to find the field template that applies to your field.
By creating your own custom field formatter by using this blog post. This will display the formatter in the dropdown as you intend.
There is also a module which helps your create custom formatters, which are ctools exportable. Which means you could easily featurize them. More about the module:


  The Custom Formatters module allows users to easily create custom CCK/Field Formatters without the need to write a custom module. Custom Formatters can then be exported as CTools Exportables/Features or Drupal API Formatters.