Genesis Accord

Hello all, I am a noob to tire and wheel knowledge. I recently noticed I need new tires. I have a dilemma, about a year ago I purchased 15" Alloy Wheels from a 1997 Acura 2.5 TL. The stock tire size for those wheels is 205/60/15. I have had two wrecks the past year, I feel the 205/60 tires make the car to bouncy more less a road wagon. When I had the old steelies on it I never had a wind tunnel feel when I got stuck behind trucks on the Interstate, now I do.
The Accords original tire size is 185/65/15. I'm in hopes that size tire will fit on these wheels without any problems. I am also looking into a lower profile tire for these TL wheels, to accommodate for better handling. Any help is greatly appreciated. Thanks in advance!