Toby, I have actually done team building using magic at a corporate event a few years ago. I will share what I did, but the practicality of it will depend on how many people there are and other factors. Also, there were four of us magicians hired for the event. The group of roughly 50 people was broken down into sub-groups (teams) of about 12 people each to prepare for a contest. Each of us magicians was responsible for teaching one of the teams (privately) a self-working, but good, card trick. Each team then had a workshop where they all practiced the trick for a few minutes with their own deck of Bicycle Standard playing cards, provided to them (paid for by the company). The magicians stayed with their team during this process in case there were questions, or help was needed - but mainly let the group sort it out among themselves. Each team then nominated one person to be the presenter/"magician" for the team and he/she would rehearse in front of the team with everyone giving feedback to help strengthen the trick and presentation. This whole rehearsal/feedback process process lasted about a half hour. Then, everyone got all together for a show, that was actually a contest. (Everyone knew in advance that it was going to be a contest among the teams)
The presenter from each team got up before everyone (all 50 people) and performed the trick that had been designated for his team. At the end, everyone voted for what they believed was the best performance. You could not vote for the presenter for your own team. The members of the team whose presenter won the contest (i.e. who received the highest number of votes) all received a nice prize (again paid for by the company).
So, I am not sure how you would adapt this if there was only one magician at an event, but hopefully it will trigger some ideas for you...
