Even though my parents and I have not stayed at Fort Wilderness, I would assume you would need some soart of card because the rule for PM EMH is to get the wrist bands you need to show them as proof that you're an onsite guest.
I think in the official Birnbaums guide to WDW they claim you need show you're KTTW cards as proof to use WDW transportation, however they never ask for it. They also say the same thing about show you're park tickets, however once again they never ask for those. So the answer is nothing is needed when using WDW transportation.