Thanks for your responses, all! So far, the only shanty I've found that mentions cats at all is "Cape Cod Girls" (nothing in it about their toes, though, just their tails). Here's a version that varies slightly from the one in the DT, from this page: http://sailorsongs.com/cape_cod_girls.htm

CAPE COD GIRLS

Cape Cod girls ain't got no combs  heave away, haul away
They comb their hair with codfish bones heave away, haul away

CHORUS: Heave away my bully, bully boys, heave away, haul away
Heave away my bully, bully boys, and were bound for South Australia

Cape Cod boys ain't got no sleds. heave away , haul away
They slide down hills on codfish heads, heave away, haul away...CHORUS

Cape Cod doctors ain't got no pills, heave away, haul; away
They feed their patients codfish gills, heave away, haul away...CHORUS

Cape Cod cats ain't got no tails, heave away, haul away
They all blew off in Cape Cod gales, heave away, haul away...CHORUS

Cape Cod women don't bake no pies, heave away , haul away
They feed their babies on codfish eyes, heave away, haul away...CHORUS