It is definitely The Kobayashi Maru. by Julia Ecklar.
The incident you refer to is a training exercise at the Starfleet Academy. Sulu and a bunch of other cadets were assigned to a role playing game, simulating the politics of the Federation and some non-Federation planets.
Sulu was assigned the role of a non-aligned planet with various problems. His assigned goal was to get the Federation to accept his planet into the Federation.
Sulu used paper airplanes and origami cranes to deliver messages to other players. As he was playing the part of a non-space faring planet, he was not allowed to go visit other players in the room or to yell across the room for communications.
To get aid from the Federation, Sulu's planet needed to first get in contact with a planet that has space travel and connections to the Federation.
At the end, Sulu is singled out for having used creative methods for trying to solve his planet's problems - along with a comment that the other players should be glad that he hadn't resorted to terrorism. This causes Sulu to somewhat sheepishly crush his last origami crane - he had written something like "I am a suicide bomb" on it, with a countdown (he ran out of space for the final "boom.")
One of his paper airplanes did in fact reach the cadet playing the part of Vulcan. By the rules of the game, it counted as "communication." This caused Vulcan to have to "sit out" one round while considering the content of the message. This cheesed off the other members of the Federation who were counting on Vulcan to solve certain problems - because of Sulu's paper airplane "communication" some of the planned solutions were delayed by several "rounds."
It's a very good book. Read it if you can find a copy.