There are plenty of other tasty selections when doing Drinking Around the World, besides beer.
Mexico: stop at La Cava del Tequila inside the Mexico Pavilion. It at the bottom of the right ramp as you enter the indoor marketplace area. They have a wide variety of Tequila shots and flights (remember, this is only your 1st stop) as well as some really delicious and different margaritas.
Norway: Inside Kringla Bakery they have alcoholic coffee drinks as well as a Scandanavian liquor called Linie Aquavit Glacier, which is a personal favorite of mine. They also have some non Scandanavian wines. The liquor and the wines you can also get at their cart.
China: The Joy of Tea is located over by the lagoon across from the China Pavilion and they have
specialty cocktails The Peach Snap and the Canto Loopy are made with juice and a shot added by the Cast Member.
If they have it, The Tipsy Ducks in Love is their specialty. It has a chocolate flavor with bourbon in it. If you go inside the counterservice which is located behind the Nine Dragons, you can get Plum Wine.
African Trading Post: Offers draft beer that can't be found in other areas of the park, but since you said that you aren't a big beer drinker, you might be interested in the smoothie with Starr African Rum.
Germany: of course it offers German Bier, but if you aren't into Bier, then you might like one of the shots they offer at the cart acoss the promanade. Jägermeister is included! The Wine Cellar shop features a nice selection of German wines with the option of doing flights.
Italy: There are a few places were you can get your drink on in this pavilion. The quietest would be Tutto Gusto Wine Cellar, located behind Tutto Italia, on the left side of the pavilion. They have quite a nice selection of wines and Italian specialty drinks. However, if you just want to grab a glass of wine and go, then Enoteca Castilla is a nice place to do so.
America: Of course there are the standard domestic beers, such as Bud Light and Sam Adams, but if you are into Craft Beers, you are in luck... they have a new Craft Beer Stand. Of course, I keep forgetting that you don't like beer, but they still have something for you. The Jack Daniel's Frozen Lemonade at the Fife and Drum is very tastly and quite good on a hot day.
Japan: In the back section of Mitsukoshi, there is a sake tasting where you can sample different, small quantities of your favorite. However, if you would like a larger drink and know what you like, stop at the kiosk outside on the left side of the pavilion. They have Japanese specialty drinks, as well as sake.
Morocco: Stop at Spice Road and try their Sangria... very tasty! They also have Moroccan specialty drinks, as well as a full service bar that can make you just about anything you like.
France: Choose from wine, champagne or the Grey Goose Citron and Grand Marnier Orange Slushes, which most people swear by. Not a favorite of mine, but hey... if you go to the ice cream shop in the back, they will serve you 2 scoops of ice cream with your choice of several liquors over it. Now, that's what I call a real frozen treat!
United Kingdom: Do Not pass up stopping in The Rose And Crown for a beer, a cider, or maybe you like Scotch... they have McKellan's aged scotch by the shot.. A bit pricey, and after drinking around the world, not a way I would have my 11th drink, but hey, to each his own.
Canada: Unfortunately, the only thing you will find here is beer, but oh, what a beer they have!!! At the new Unibroue cart there is a beer called La Fin Du Monde... and since this is the end of your drinking around the world, it is a perfect ending, since it translates into The End of the World. This Belgiun Tripel goes down more like a sparkling wine than a beer. It and it's sister, Maudite, which you can only get inside at Le Cellier, are my 2 favorite beers in the world...... they just AREN'T "beer-y". If you don't want a whole one, take a sip of someone elses.. Hey, as long as you taste, it counts, right?
Now, if you are more of a beer drinker, as I am, then you might want to start in Canada and make your way around the other way... that way you remember those things you REALLY liked, and if by the end, you aren't as into it, or just can't drink another drop, you haven't missed your favorite.
Hope you enjoy your trip around the World Showcase, and remember, make sure you hydrate with water in between all of those drinks and eat, as well!