I have a long, narrow 'surf ski' kayak that's fast but too tippy when stationary let alone swivelling at the hips with a camera.
But I also own an ideal photography platform - a fishing kayak. They're wide and very stable.
The longer ones can cut through the water and often have rudders.
The shorter ones can have trouble 'tracking' and it's difficult to go decent distances since you tend to zig zag your way across a lake instead of go in a straight line.
Sea kayaks are wonderfully stable ... here my wife at the front doesn't appreciate me putting down my paddle and getting the camera out ...