You should be able to alter the logo-path in hook_preprocess_page and replace the logo path with the path of the transformed logo:

function mytheme_preprocess_page(&$variables) {
  $variables['logo'] = image_style_url('my_image_style', $variables['logo']);
}

Didn't try it out, but it should work somehow this way.

edit: there is a LOT of "logo" in my first sentence ;)

You should be able to alter the logo-path in hook_preprocess_page and replace the logo path with the path of the transformed logo:

function mytheme_preprocess_page(&$variables) {
  $variables['logo'] = image_style_url('my_image_style', $variables['logo']);
}

Didn't try it out, but it should work somehow this way.

edit: there is a LOT of "logo" in my first sentence ;)