If you're looking for ideas that don't revolve around alcohol but incorporate your theme, that shouldn't be too hard.
I guess it depends on where you're holding your mixer and how much is in your budget...but let's say you had permission to hold it at a banquet hall and wanted to do a dinner. Since your theme is Around the World, maybe coordinate sisters into groups of like 5 to 10 and each group makes a different ethnic food. I don't know if you want to ask the participating fraternity to do the same...but then you can lots of different types of food (don't forget deserts). Then you could serve virgin alcoholic-type drinks. So for instance to go with the Mexican theme, serve virgin margaritas. To go with the American cheese burger, a coke would be simple. Or you could do tea with chinese food. Then you can have table decorations to coordinate with each country. Maybe to make it fun, each group could try to dress like the ethnicity their food represents. Don't forget Greece (TOGA TOGA TOGA).
I don't know how else to incorporate the theme without food...so this is just my idea.
Hope that's what you were looking for!
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