Internet popularity poll. As usual, more/most of the plain “shanty” returns are off topic. The plural “shanties” is the other way around but still a smaller return.

archive.org metadata, audio
Shanty: 1,071
Shanties: 198
Sea shanty: 148
Sea shanties: 119
Chanty: 52
Chantey: 35
Sea chanty: 15
Sea chantey: 13
Sea chanties: 13