Tires alone can make a HUGE difference in traction. You might not actually need 'wider' but just sticky.
Personally, unless you plan on some hardcore racing, I would waste your money on tubing to put 10" wide wheels on this car. You can get the stock 17s modded to 9" wide and only need a small spacer/maybe fender rolling.
Keep in mind, the wider/sticky tires will also beat on your drivetrain more. You might drop the DS or an axle if you go to agressive without the supporting mods.
2003 Corvette Z06 - MGW shifter, Corsa X pipe, Corsa Xtreme exhaust, Texas Speed long tubes w/o cats, PowerStop rotors/pads, Conti DWS tires, C6Z51 F&R sways, C5R headlights, tuned
04 GTO - sold