It is legal, and the only reason cowlings and internal baffles are designed to force air over the cylinders is because that is necessary
when there is a cowling.
Banner-tow airplanes don't fly without cowlings (or baffles) because their owners can't afford cowlings... it cools the engine much better, and the aerodynamic penalty is negligible because they are not trying to go fast (and can't, really, towing a huge, draggy banner).
The remaining part won't come off if it is attached properly, but with this particular Cessna I do see one problem: no air filter. You wouldn't want to operate that engine for very long without one, and I think most banner-tow airplanes have some sort of rig to keep a filter on the intake despite the lack of a cowling.