Indoor rock climbing may not be entirely relevant to skills, but should help with team building. While it's an individual sport, there are many ways to make it a team exercise or competitive event depending on what you're shooting for.
Tape game: Each person takes turns clearing a route. As they go up, they tape off one of the holds - no cheating, you can't tape a hold after you've used it on the way up. The last person able to successfully scale the route without touching a taped off hold is the winner.
Climb blind: Pair up and discuss the best way up your route. One person will be the climber, the other the guide. Blindfold the climber, get him to the first hold, and let the guide talk the climber through the climb. This one is generally done as a timed event to promote good communication and listening skills, as well as trust. Switch roles, then record the combined time. The pair with the lowest time wins.
Many gyms offer group rates, and if no one is qualified, you can generally arrange some instruction as well. This is a good blend of flexibility and strength conditioning, as well as team building and problem solving skills that may be useful for killing some downtime.
Again, I'm new here, so I apologize in advance if this activity is inappropriate.