I saw a ad for this show and in the quick blink of an eye I seem to recall seeing them shooting Matchlocks.
Although the Wheellock and Snaphaunce was being used by this time, I think the Matchlock would be period correct for some of the pilgrims in 1620.
In the book "THE MAY-FLOWER & HER LOG",by Azel Ames, M.D.,©1901, Azel Ames on page 227, the author writes,
"...The arms and accoutrements [sic] (besides ordnance) of the May-Flower Pilgrims, known on the authority of Bradford and Winslow to have been brought by them, include muskets ("matchlocks"), "snaphances" (flintlocks), armor ("corslets," "cuirasses," "helmets," "bandoliers," etc.), swords, "curtlaxes" (cutlasses)," "daggers," powder, "mould-shot," "match" (slow-match for guns), "flints," belts, "knapsacks," "drum," "trumpet," "manacles," "leg-irons", etc., etc. "Pistols" (brass) appear in early inventories, but their absence in the early hand-to-hand encounter at Wessagussett indicates that none were then available, or that they were not trusted...."