Will C-6 wheels fit on a 96 C-4 without too much hassle

I think the offsets are different.

If you know the offsets and widths of the C6 wheels your using I can answer that question.

Offset being, the area where the wheel meets the hub and the area where the tire meet the wheel, offet is this distance?

No. It's from the imaginary centerline of the wheel to the mounting surface on the hub. Usually easy to find. Both width and offset effect fitment.

I googled C6 wheel offset that and found this:

Base model front: 18x8.5 offset: +56 mm
Base model rear: 19x10 offset: +79 mm

The fronts will fit the same as your stock fronts.
The rears will tuck in 3/4" more than your stock rears and will need an adapter to look right.

On my least favorite place to shop, ebay, they sell spacer/adapters 3/4" for $59.00 plus $5.00 for shipping for two.

Find a seller with 100% positive feedback.

If you get reproduction/chinese wheels, you sometimes can't use adapters that are thinner than the 1-1/8" stock wheel studs.

If you get OEM c6 wheels, you're fine.

Fronts are 8.5 rears 10, thanks for all the information, so quick!

After thinking about it for a bit, this is the only place where you can get the correct info so fast, thanks again.

go to lakeshorewheelandtire.com And click the "corvette specials."

There's lots of misinformation on wheel fitment out there, so beware of what you hear elsewhere.