The green light probably has a "don't walk" symbol for the crosswalk, unless someone has activated the crossing signal. At this point on your bike, you could act like a pedestrian, and press the button to change the walk signal. This is probably your safest bet, since after all, it's basically a modified sidewalk you are on, and you're expected to cross in the crosswalk, with pedestrians.
Sometimes you have to cross on the left side of the road, which is even more challenging.
Talk about living in an auto-centric universe!