URL for cron Jobs gives me a 404 error
Two answers:  First, yes, changing the permission should be safe to do.  Note, however, that you'll have to repeat this process every time you upgrade.

Second - this isn't a normal restriction, so I'm guessing you're running CiviCRM on shared hosting.  The change you described removed the "group owner can write to this file" permission of cron.php.  You did NOT change who could read or execute the file - so this shouldn't have had an effect.