I own a Hobie now for kayak fishing, but I used to just kayak/paddle on a sit-in. My advice may not be too helpful since sit-on-top kayaks sit a bit higher then sit-in kayaks.
I was taught not to use my wrist at all when paddling. There were two concepts I remembered that may be useful.
First - when you paddle you are actually using your torso to move the paddle through the water. Your arms will fatigue sooner than your body will. Go grab a paddle and a big inflatable ball and sit on the ground. I'll wait....
Now go ahead and hold the paddle in your hands like you are going to paddle out to Lake La Jolla. Wedge the ball between your chest, arms and paddle; or imagine there is one there. Now pretend to paddle. You notice you have to dip your paddle into the water by moving your torso and twisting your body. Many paddlers do not twist their torso, but just move there arms. There should be very minimal arm movement when paddling.
Second - Most paddlers use only a push movement when they paddle when they can use a pulling action at the same time, thus sharing the burden of moving the paddle through the water. This concept is really hard to describe yet very easy to show. Go grab your paddle again. If you are putting your left blade into the water you would pull with your left hand as well...but wait. You can also push the paddle with your right hand at the SAME time. If you do this you can move the paddle through the water using a push and pull movement and NOT just the push movement. If I was to freeze frame your hand posture in this example above your left hand could be in a cradle (not fist) and your right hand could be an open palm. Now you wouldn't paddle this way, but you can do this to visualize the idea I'm trying to show. This concept is really useful when you are cruising and not necessarily looking for a burst of speed. For example, don't do this while your are launching through the surf.
Your legs and knees come into play as well, but I think it is more pronounced with sit-in kayaks. The basic idea is to paddle with your body not just your arms/wrists.