C7 Z06 wheels aren't even close unfortunately.
Your stock setup is 19x11, 19x12 with 305 front and 325 rear. Keeping the nannies happy will be accomplished as easy as possible with stock size tires. I'd recommend Michelin Pilot Sport 4S tires in stock tire sizes on OEM size wheels. OEM wheels are an option, new expect $2500-$3000. There are some Replica options, check
Phastek for that. Looking for aftermarket forged wheels wouldn't be a bad way to go, but costly, expect $6,000-$12,000 a set. You could also run stock sized "regular" ZL1 wheels/tires. MRR makes a replica of the ZL1 1LE wheels in 20" sizing, Phastek sells them.