i've done some different team building stuff, it varied from place to place, two of the faves were the spiders web, and sheparding. both are good fun and involve a bit of thinking to say the least. have a look round, lots of places offer team building stuff, some places offer dedicated team building instead of bushcraft/survival courses. as you don't want advertising, i won't mention the one i'm thinking about. if you want more info, let me know and i'll point you to the courses that i've been on. hope your quest goes well.
never send for whom the bell tolls, it tolls for thee.