If you plan to install an in dash CD player, you will have to alter the radio bezel for the DIN mount. If you look around some of the Corvette swap meets, you can sometimes find one that has already been cut. That way, you won't have to destroy your original.
Chris (69 my way) may have some suggestions for what to do . . . he's got the thump, thump goin' on in his . . .
Did a little research on this for my 77 a couple of months back. Was told that an aftermarket CD player is wider than the stock cutout in the dashboard and you can either cut it, which I don't think you want to do, or add an aftermarket radio, similiar to a home stereo, with jacks to add a changer elsewhere in the car. Several places on the Web appear to have these type of units.
You may want to investigate the "add on cd changer" option.
They work with your existing radio and AMP if you have one. Some must link to a separate "rf modulator" that you hide somewhere, some new ones have the rf modulator built into the changer from what I understand.
This is the option I use, pretty nifty, works great, the drawback is you have at least 1 added component to put somewhere in your vette
If you want the original look, and no cutting, go for one of those hidden/secret sound radios. These things work off of a wireless remote and the actual radio and disc changer can be in a cubby or back compartment area.
Otherwise, you will be cuting the dash to make an indash one work. I had to cut mine, and off set it by about 3/4" to clear the vintage air system.
A new center dash piece from Paragon is about $90. If you are concerned about originality, remove you stock system and center panel. Buy a new panel, hack it out, and enjoy your tunes. If you ever sell the car put the old one back.
The only problem with swap meet center panels, is most of them are already snapped in the upper section, and if they are not the vendors want as much or more than you can buy a new one. I had no choice anyway, mine had already snapped on each side in the upper portion like 88% of the others out there.