Nobody (more or less) today sings chanties when they sail in extant ships, large or small. Habitually, I mean. Because chanties are not "needed" as such, there is really no reason to assume anybody in the past sang chanties if documentary evidence does not say they did.

Nor, to my mind, is there any reason to assume that someone on a ship would sing any songs they wouldn't sing while not on a ship. One might as well assume that Blackbeard sang beard songs or robber songs or washing dirty laundry songs. Focusing on the fact that Blackbeard was sometimes on a ship erroneously assumes that he sang some special ship songs, followed by the erroneous assumption that ship songs means chanty genre songs. What rock 'n' roll songs did Abraham Lincoln sing?