As for cockney, I think not; the construction using "what" (or "whut") instead of "that" is not unusual in Ozarks and Appalachian colloquial language.

The colorful and oft-borrowed image of lowering him down with a golden chain and digging his grave with a silver spade is found in many Appalachian songs of English descent, of which "Old Blue" comes to mind as a ready example.

I would be willing to bet that the song does derive from memories of English sailor ballads in some way although I cannot tell whence, if we but knew the stages of its descent more clearly. What a foggy business the folk process is sometimes! But the rhythm is not suitable for a working shanty. I could hear ity as a foc'sle head lament for the off watch on a broad reach in fair weather, though.

A