You get non-alc beverage on the
DDP, then you pay the difference out of pocket for the souvenir mug. It may not exactly be the difference, but they will have a price near enough to it that they charge for the stand alone souvenir mug.
On several occasions I have heard people say that the only way to get a souvenir cup or popcorn box is to pay full price out of pocket but I buy 4+ souvenir food package items each trip. Last trip it was BB-8 sippy, Han Solo Carbonite Popcorn box, Country Bear Jug, Jungle Skipper Canteen Mug, and 4 tiki mugs from trader Sams. I always get the item on DDP Snack Credit or as a bev. then pay up the difference for the souvenir item.
The souvenir item is usually a nice round number so like at the Jungle Skipper the Punchline Punch is $4.50 and with the mug it's $13.50. I don't remember directly but I'd bet my shoes they will sell you the mug for $10.
Sometimes you get someone new behind the register who latches on to the idea that you can't use DDP to buy souvenir items. That's fine, conduct the business of buying just the non-souvenir version with DDP then ask if they will sell you the souvenir item all by itself.