I distributed my first Golden Ticket last week. Definitely helpful to have something physical to exchange - my FA commented she'd heard of them, but never actually been given one before. I could hear the CSM commenting "that was well deserved" during final approach too.
If you're looking for an opportunity to make the exchange as seamless as possible (ergo, not awkward) I'd suggest during meal clear up of the final meal service prior to arrival on long haul? Things are moving quickly at that point, you've likely made up your mind, and it's a natural point to take something away
