Paddle out of the room and turn left.
Try to steer along with the current so you're always facing downstream. This will give you a little more control of the boat. Continue around the corner to the right...
...past the ledge with the second button.
As you turn the next corner to the left, try to stay in the middle of the channel so you can snag a save/power-up crystal. Keep to the middle or right side as you pass under the wooden bridge and over the next small waterfall.
Make a tight paddle turn to the right at the next corner (hold Walk + Right) to avoid the red tripwire beyond the large boulder.
If you do accidentally go over the tripwire, try to back paddle to avoid being crushed by falling rocks. Once they've settled, continue past them.
As you move out into the slightly calmer pool ahead, steer to the left to cross the green tripwire, which deactivates the slicing blades on the right.