I'm gonna get beaten for this, but...

Just about any of the 'call and response' shanties (Haul away Joe, Paddy Doyle's Boots, One More Day, etc., etc., etc...) can be cleaned up for children. I've sung all of these and several more, and we sing them as straight improvisational songs, with the chorus being sung by the group, and the verses being made up on the spot. They can be as dirty or clean as you want them.

If you're looking for straight, traditional shanties, then the pickings are a bit more lean. The Dead Horse shanty comes to mind... Paddy West should work (depending on the version, there may be one or two alcohol references, but there are plenty of bowdlerized ones as well), and a personal favorite of mine is Leave Her, Johnny, which most versions I've seen have very little in the way of "objectionable" material. Actually, another good song that may or may not be considered a "shanty" is Rolling Home. It apparently existed on shore first, but was picked up as a forebitter by the sailors.

Hope this helps...

M