That same Greatful Dead site has what seems to me to be highly credible explanations about the meanings of several terms and phrases used in the Iko Iko song. Maybe I shouldn't be surprised about this, but I admit that I am.

Check out these excerpts:

..."chicken wire" is what it sounds as if Jerry is singing (though on some other versions it sounds more like "chicko wiyo"). I haven't tracked this line down to any definitive "source" in other versions. Reg Johnsey came up with this explanation:
The way country people celebrated Carnivale/Mardis Gras was to make conical masks out of chicken wire and decorate them, wearing them with costumes festooned with strips of cloth. So, the references to fixing someone's chicken wire sounds like a joking threat to mess up their masks, since part of the battle was how good the costumes were."

"Joc-a-mo-fee-no-ah-nah-nay, Joc-a-mo-fee-nah-nay" is a ritual chant used by the Mardi Gras Indians which has been around for so long the words are no longer clearly distinguishable, and it has a well understood meaning of its own. Very, very loosely translated it signifies "we mean business" or "don't mess with us". Originally it would have been Cajun (a liberal mix of French and English) and literally translates to "the fool we will not play today"...

One additional comment on the origins/meaning of "Iko":
"Iko and un day are Creole corruptions of the Gambian call ago! [pay attention] and the expected response, which is amay! [I/we are listening]. Chuck Davis of the African- American Dance Ensemble, which is based here in Durham, uses this device ubiquitously when he acts as Griot (master storyteller/master of ceremonies). When he calls "ago!" everyone is supposed to shout "amay!"--no matter what else is going on. He likes to slip this into the middle of various narrations just to make sure folks are paying attention. He also uses it as an introductory, "calm down" sort of exercise before he starts to speak, or to quiet the crowd if it gets noisy while he's speaking." ...

-snip-

BTW: I've frequently heard the call "ah-GOH!" and its response
"ah-MAY" {both spelled phonetically} are used with children by Afrocentric cultural groups in Pittsburgh, PA and other US cities since about the mid 1980s for the same reasons as mentioned in the comment above.