I was just watching Voyager and had an idea for a new shuttle event. In the episode Drive (S7E3), the Delta Flyer gets entered into a race to symbolize peace for a few races in the Delta Quadrant.
I think there should be a shuttle race event that takes place during special events. In the last Winter Wonderland, the foot race was added, so it is not a stretch to modify the mechanic for a shuttle race event.
To add some additional flavor to it, I think there should be special shuttle impulse engines that are tied for racing. One engine could have a better turn rate, while another could accelerate faster.