Way to have a theme-settings form input to accept numbers only?
You should be able to add your own validation handler. After the code you've shown, add this:

$form['#validate'][] = 'my_validation_handler';


Then in your handler, you can add your own validation:

function my_validation_handler($form, &amp;$form_state)
{
  if(!is_numeric($form_state['values']['mysite_contact_phone']))
  {
    form_set_error('mysite_contact_phone', t('Contact number must be numeric'));
  }
}