How to skip no data to update exception?

try/catch.

v4.3.0 will have allowEmptyInserts() method.

Do you mean to leave the catch empty,  something like this?

PHP Code:

try{
  $model->save($entity);       
} catch (\Exception $e) {
    // LEAVE THIS EMTPY
}

//other stuff that will be processed even when an Exception is fired.