It is indeed an interesting idea. It invites the invention of some sort of scenario that might have happened if the ship had been preserved (as she certainly should have been).
Most American warships of WWII got substantially modified (if they didn't get scrapped) shortly after the war - for several reasons. Those that remained in active service had to be modernized, in order to keep up with the state of the art in such things as electronics and armament, as well as tactics and strategy. Battleships, for instance, lost their catapults because the use of fixed-wing spotting aircraft launched from battleships was obsolete. And thousands of 20mm Oerlikon anti-aircraft guns got removed from warships of virtually all types, because the Navy had concluded that it just wasn't an effective weapon any more. In many cases the 40mm Bofors guns went too, to be replaced by the more efficient 3-inch.
Ships that were to be mothballed also had many of their open-mount guns removed, because (I guess), preserving them wasn't considered to be worth the trouble (though there are lots of photos of mothballed warships with their 40mm mounts covered by "domes," made from some sort of material that was sprayed onto a metal framework built for the purpose). And, of course, virtually the whole fleet got repainted. I have the impression that the various WWII camouflage measures were gone within a year or two (maybe somebody can correct me on that point), replaced by a uniform grey with big, white, black-shadowed hull numbers. (A generation of Americans came to think that U.S. warships had looked like that during the war, largely because of the Hollywood movies that were made in the fifties using ships that kept their current color schemes during the filming. Heck, if it's big and it's grey and it floats....)
So are you going to assume that the Enterprise remained in service for a few years after the war? If so, she probably would have gotten a new radar and communications suite of some sort, lost all her 20mm guns, and, of course, gotten a new air group. (Skyraiders and Bearcats, maybe?) And she would have been painted overall grey, with big, shadowed hull numbers - and probably big, bright-colored flight deck markings (on unpainted fir deck planking). And conceivably some big, ugly modification to let her accommodate the new generation of airplanes. (A deck-edge elevator, maybe? Or a big, glassed-in bridge structure?) But if the organization funding the restoration had enough money (hey - we're talking pure fiction here), maybe it would have scrounged enough 20mm guns from various sources to replace the whole late-war anti-aircraft battery, and repainted her in one of the schemes she wore during the war. Or maybe the restorers decided to take her back to her as-built configuration. Or maybe they did their best to make her look like she did at the Battle of Midway - with a reduced 20mm battery and 1.1-inch "Chicago pianos" instead of the 40mm Bofors guns. Or, more realistically, maybe the organization was strapped for cash and left her with no 20mm guns, the color scheme she wore when she was turned over to them, and her superstructure in whatever condition it was in when the Navy got through ripping out whatever electronic equipment it could use elsewhere.
It's an interesting exercise - and a sad reminder of what that generation failed to save for us. Maybe, though, we should also be reminded to be grateful that so many American warships of WWII did get saved. The U.S. obviously has far more of them, of more different types, than any other country has.
Good luck.