Honestly, I don't think I've ever heard of either "...I am giving you his regards..." or "He is giving you his regards...". The most common thing to say would be "You have regards from...[him, her, John]"
About "Let him know" and "Give him this message", I guess I would say "John/Jane/Santa wants you to know that..." and "You have a message from John/Jane/Santa"...
EDIT: Hmmm..Or would be.. I'm not so sure now even for "You have regards from". I think I would just say "Regards from"...Let's wait for more opinions, shall we..
