Considering buying small whitewater kayak for small lake
for better maneuverability and different types of workouts
dont care about speed or distance
not sure if that would be a mistake
I already have a regular recreational lake kayak
Just a couple weeks ago, I met a friend on a local flatwater lake after a river paddle in my whitewater kayak! It isn't impossible and it certainly is a workout, so it might be right for you if that is your main goal. Many people learn and practice different whitewater skills on flatwater, so that could add to your types of workouts. If you get a sprayskirt and are comfortable wet exiting or rolling (or learn to roll), you open up your world to a lot of new kayak based workouts!
As for maneuverability, it is certainly more nimble and responsive to paddle a whitewater kayak, but on flatwater that means you have to correct yourself with almost every stroke. And I'd be lying if I said I didn't end up spinning my boat once the other day! Most whitewater boats are flat on the bottom and designed to slow you down, so you have time to make your moves, this means they have nothing to get you to track, meaning go straight. If you are used to a recreational kayak, you will have a long time adjusting to how to paddle this type of boat on flatwater. I wouldn't necessary call it maneuverability that you gain, but the boats are certain more responsive.
Here are a few other things to consider about a whitewater kayak:
If it were me, then I would only go for the whitewater kayak, if I had interest in learning how to whitewater kayak. Otherwise, a short recreational boat would be best. Good luck and hope this helps!