is there a way to overwrite the views Sort criteria?
Sure, just use hook_views_query_alter().
You can intercept the view's query object and make any changes you need to it, including (but not limited to) adding/removing sort criteria.

Better WHERE's for your Drupal forums with hook_views_query_alter and Using hook_views_query_alter to change your views sort order give some examples of how to alter a view query.