Peterson wrote a book about this period : "Arms and Armor in Colonial America 1526-1783"
Not much on the Pilgrims, but they did have match locks and a few had flint arms, which were snaphaunce locks.
The book shows a snaphaunce lock excavated at Jamestown.
Peterson also wrote : "Arms & Armor of the Pilgrims"
He says there are no records which positively state wheel locks were at Plymouth and no relic wheellocks survived. It is a could be for wheellocks. The Pilgrims used "fowling pieces" and pistols. In 1677 the Plymouth General Court outlawed the matchlock, so Peterson concludes the snaphaunce was the principal ignition system by then.
Some stuff here:
I would say, just look at the arms of the British Civil War and you will see the same equipment at Plymouth.