As several people have already pointed out, "battlewagon" is just slang. The actual 'class' of the ships in Action Stations is "Battleship". That's slightly confusing in and of itself, since 'battleship' is later used by the original Wing Commander to describe *any* line warship (destroyers, cruisers, etc.). At 50,000 tonnes the battleships of Action Stations are more than twice as large as the most powerful cruisers that show up in the games. Operationally they're more akin to the Gettysburg-class or Concordia-class cruisers/supercruisers which appear in Freedom Flight and the movie respectively (though they don't carry any fighters at all).
My notes say that the only weapons referenced in the novel are three forward plasma batteries, missile launchers (when the Yorkshire is fighting a pair of Gamorgin-class ships) and mines (when the North Carolina jumps out of the McAuliffe System). The Kilrathi Zulu-class battleships are said to have particle and laser cannon batteries which they use for ground support.
There's no name for the specific class of Terran Confederation battleships - five specific ships are named in the course of the game (TCS Belarus, TCS Gibraltar, TCS Malta, TCS North Carolina and TCS Yorkshire). Three separate classes of Kilrathi battleship are mentioned (Gamorgin-class, Yar-class and Zulu-class). One individual ship is mentioned - KIS Kitagki.