This is one of those questions that requires a book to answer satisfactorily.

Is there a comprehensive chart or dataset of all known WWII wrecks?

Not really. Part of the problem is that the fog of war means that some ships' fate is simply unknown. Last reported positions are difficult to square with attacks, which themselves can also be labeled as the wrong position. Researchers used to think that U-869, the subject of Shadow Divers, was sunk off of Africa while its wreck is off the coast of New Jersey- quite a big difference! The submarine I-12 is another example of this phenomenon. It is possible an American task force sank her in November 1944, but the IJN did receive a possible transmission from her in January 1945. I-12 may have survived her November attack, but have still succumbed to another attack or operational failure and was last with all hands.

All of this makes cataloguing losses and positions very difficult. There are some websites and organizations that do try though. The history.navy.mil site has a listing of American submarine losses as well as Japanese subs. wrecksite.eu is another great resource that tries to keep updated on wreck discoveries. U-boat.net is a fantastic resource for the battle of the Atlantic. Pacific Wrecks covers not only warships, but also some aircraft wrecks such as listings of Aichi E13 wrecks.

But a perusal of these websites reveal that this is only scratching the surface of wreck sites.

How many of the shipwrecks are submarines?

While the losses of submarines is pretty well established because the Allies demanded the surrendering Axis account for all war materials- you can check surviving hulls against navy lists- where and how all of them sank is still a mystery. U-boat.net is probably one of the better sites for mapping and listing known sub wrecks. The site is fairly old and well-established and had more than just U-boat wrecks.

What percentage of WWII shipwrecks are in shallow water vs open ocean?

This is one of the factors that makes finding these wrecks so difficult. WWII was in many respects a blue-water war meaning that a lot of the fighting was in the open ocean. This means that a fair number of wrecks are quite deep. This poses a problem for exploration as both pressure and the scale of the ocean are huge obstacles. Although it is a bit snarky, this XKCD comic does highlight some of the real problems depth can pose for maritime archeology. Exploring the ocean floors is time-consuming and requires a great deal of financial backing. The RV Petrel- see its FB page has made a lot of waves in the past few years with its discovery of the USS Lexington and the superbattleship Musashi among other wrecks. Petrel's backer is Paul Allen, a billionaire whose net worth is $20 billion according to Forbes. Having a patron with deep pockets is pretty important for this type of exploration.

But even with such funding, there are a lot of big wrecks out there. For example, of all the Japanese carriers sunk that were not salvaged postwar, only one- Kaga- has been located and that was only a partial discovery. Some of these wrecks are very deep and while that may preserve some of their features (Yorktown was especially well-preserved) it makes them a real bear to discover.