Hopefully not to sidetrack this thread too much :
Are wreck certifications "required" in the same way that cave certifications are? Do boat captains ask to see a card before going to a specific wreck?
There's wreck diving, and then there's wreck diving.
At one extreme, wrecks like the Copenhagen in Florida should be called "wreckage diving." It takes nothing more than the most basic OW skills. At the other extreme are deep, dark wrecks with labyrinthine passageways that require special equipment, decompression skills, and advanced wreck navigation skills.
Most wrecks are well in between those extremes.
By far the wrecks most people dive are on the recreation side of the spectrum. They are not all that deep, and most penetrations have an easily seen and easily reached exit to open water nearby at all times. No special certifications are needed.
If you casually go to a recreational diving web site and they offer trips to local wrecks, they will almost always be accessible to an open water diver with no special certification needed. If the wreck does require some technical skill, you will usually be warned in advance.