It's impossible for me to know your skill level, but it is pretty easy to accomplish.
I have a two pulley that I put on my car probably 10 years ago and have never suffered any ill effects, even in heavy traffic in the Texas heat. I have made lots of small mods that have added up and my car is pretty quick for having an engine that has never been opened up further than the plenum and injector rails. A side benefit of this mod is that your accessory will last longer.
I have changed belts on a number of cars and I don't remember if the Vette is one that needs the slim tool for loosening belt tension or not. If I remember correctly there is room to use a 1/2" breakover on the tensioner to lever it up and remove the belt. I might be wrong though. You can get a tool for this job off the tool truck for about $30, or it might even be available for less at the parts house. Then changing the pulleys is a simple matter of removing the bolts and swapping the pulleys.
No, you don't have to go under the car and you don't need a puller. The crank pulley will come right off after the bolts are removed. Don't remove the large harmonic balancer bolt, only the three that surround it. You might have to tap on the pulley lightly to get it off.
On the alternator a strap wrench would be handy to hold the pulley while loosening the nut, but you probably could improvise with a rag and an extra large set of channel locks.
Good luck,