I run shanty workshops for schools in my area. It is a simple matter to omit the bawdy verses and replace them with more "child-friendly" versions.

I give the children a brief history of the shanty and an idea of what life was like on board ship in those far off days and they tend to act it out when actually singing.

It's great if you have the relative props during the sessions such as a capstan. The children love heaving it around.
Their favourite shanty is "The Drunken Sailor."

I had a class who performed in the presence of the Queen and The Duke of Edinburgh on their visit to Swansea a number of years ago.