I will probably get pounded for this suggestion, but am going to offer it any way!
I think if it was my corvette, i would want to make the antenna as non conspicuous as possible..
First suggestion would be a through the glass mount antenna on the rear window.one
caveat though. Through the glass antennas are notorious for being poor both for ransmitting and receiving, but if you are mostly in a good reception area, i think the antenna would be a grat trade off as opposed to mounting the antenna on a lip mount aesthetically speaking while still doing better than you will with a duck on the scanner.
second suggestion, is what i have done on my vehicle, i have a 2/440 antenna mounted in a stake hole on my bed, but did not want to mount a scanner antenna outside. I purchased a mini 800mhz antenna with the tiny mag mount, (mag is about size of a quarter) and found that the upper should harness restraint would let me stick the mag mount there, and the antenna is vertical in the center of the rear window, out of the way, and pulls in station 20 miles away.
Both these ideas are stealthy and aesthetic, but by no means approach the reception you get with a high quality outside mount antenna, but also both of these methods can be tried for very little money so you don't have much to lose.................