The last of these ships was completed (I believe) during WW II. The information you seek may have settled pretty deep into the silt by now. New Jersey (BB-62) is berthed in Camden, New Jersey as a museum. There is an association that runs the museum (search google "battleship new jersey") someone there may be able to help, they probably have at least some construction drawings. Similar associations probably exist for the other three ships. A freedom of information request to the government might work (I have no idea how to do that but any journalist probably does). There may be more recent information- New Jersey was refitted and reactivated during the Viet Nam war.

Perhaps a project about submarines would be better. Several of those who post here were involved in construction and maintainance of submarines.
Bill

I'm also a University professor of welding. Of course, a third world, underdeveloped university that can not be compared, not even remotely, to O State U, which has given more than one Nobel Prize to Human Kind.
Nevertheless, I'll give you my opinion so you can use it as you wish.
As Bill pointed out, Kansas type warships were made during WW II, so their welding procedure is outdated.
Regarding nuclear submarines, SSBN, who's not only welded, but also sailed on them, says (and he's right) that their welding procedure is a military secret. Being a military secret means that it (the welding procedure) is not a simple one. If it was, it wouldn't need to be that secret.
Let me ask you a question. You're talking about an academical exercise, i.e., one that the students must comply with to get their degree. Here at Mackenzie Presbyterian University we also have that type of exercises. Why making them that difficult? If welding of nuclear submarines is a military secret, useful bibliographycal references must be very very scarce, and putting up a WPS starting from zero shouldn't be easy for university students, even if they are from O State.
My opinion is that you propose to your mates a more common application, one for which bibliographycal references are easy to find at the university library or elsewhere.
Examples: welding of high pressure steam piping in a thermal power plant; welding of a vacuum tower in an oil refinery.
I've got with me the complete welding procedure specification of a urea reactor in a chemical plant. Even the smallest weld has a page specifying every detail of it. I don't remember now the exact number of pages, but they must be about 100 or even more.
If you wish, I can send you a copy, and if you use it in some way I'll feel quite honored, because me, the third world, underdeveloped professor has contributed to the excellency of none less than Ohio State University, the same that has given to the world more than one Nobel Prize.
Giovanni S. Crisi
Sao Paulo - Brazil

As I waddled around the web I came upon this treasure trove of information. Though your quest is slightly different, it does provide good information that you may find helpful.
The web page I posted below has weld procedures that were generated for various materials.


http://engstandards.lanl.gov/engrman/13weld/html/13-vol3-wps_archives.htm

You might want to check out the index tab.

Rich