What is the correct creature type for Lesser and Greater Werewolf?
The creature sub type "Lycanthrope" has been removed from the game; "Werewolf" is correct as per Oracle reference.

Oracle is always the final authority on all questions about a specific card:


  108.1. Use the Oracle_(TM) card reference when determining a card's wording. A card's Oracle text can be found using the Gatherer card database at http://gatherer.wizards.com.


A rule specifically tackling your question: 


  205.3f Many cards were printed with subtypes that are now obsolete. Many cards have retroactively received subtypes. Use the Oracle card reference to determine what a card's subtypes are. (See rule 108.1.)


I don't see any way to convince other players of that fact if they choose not to believe you, except by showing them the Oracle reference. Note also that in the Comprehensive Rules, section 205.3m, there is a list of all currently legal creature subtypes, and it does not list Lycanthrope.

For reprinted cards with that issue, you could take 1 of the reprinted cards as a sample and prove it that way.