In several ways you're quite wrong. The sidwall does alot for us in the way of traction. Because it flexes, it can 'give' a little in order to keep the tread on the road. On a lower-profile tire, this can't happen as well. To get the firmer 'feel' in cornering, upgrade your suspension.
The larger wheels are more rotating mass as well, and will slow you down on a quick launch.
Work on your suspension and either get better tires or have them siped. I've run siped tires on my 93 for almost 2 years now, so the new set on it (less than 100 miles on them) were siped when they were installed.
I just had the tires on my 95 siped yesterday due to their shittyness (I didn't buy them, they came on the car) in the rain yesterday. It improved my wet grip by a good 50% (extreme case due to the crappy tires on that thing...."wingro tires".
Siping isn't generally intended for handling, but rather traction and braking in a straight line, but it does help in all conditions.
Beefier springs, swaybars, endlinks, and struts will do for your handling/cornering. Not bigger wheels.