It seems as piracy chronicles are traditionaly fancifull, and rather dificult to discern which were the actual devices tose guys used in action. According to Exquemelin's way of portraying his favorites, those operating in the Antilles, the main weapon was indeed a short piece, practical for boarding melee.
On the other hand Teach ( Black beard ) can be seen portraied in "speciality books" with various pistols ( three according to chronists ) and a full sized sword ... and two burning priming cords pending from his hat
William Kidd is a figure that still sustains lots of mystic as, just the other day, certain researchers went back to the files to try and determine that Kidd's condemnation was a judicial error
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All this and much more comes in an interesting book about Piracy and Corso from all times, published in 1997 ( ISBN 972-759-044-6 ).
A pitty that the weapons used are the least contemplated part.