The term "wreck diving" covers a wide range of possibilities.
At one extreme is something like The Copenhagen, which is near where you will be diving. You can call it "wreckage diving" to be more accurate. It is perfectly safe for divers of all levels with no additional training or equipment required.
At the other extreme are the deep, dark, silty, labyrinthine wrecks where an untrained diver can be lost in a heartbeat. The Andrea Doria is such a wreck.
Most are in between those extremes, and the value of basic recreational wreck courses lies primarily in learning the line between what is safe for that level of training and what is not safe. If you want serious training for the really difficult wrecks, you will have to go outside of any of the normal recreational agencies for the class.
The wrecks you will be diving are closer to the Copenhagen extreme than the Andrea Doria. You will never be in a situation where you won't know your way out. There will be nothing collapsing on you, and you won't get entangled in anything. The "silt" inside them is sandy, so even if it gets kicked up a lot, it just settles down quickly.
But they are fun! Enjoy yourself! If I were in the area, I'd be happy to do the trip.